ISAAC A. GARCÍA

ISAAC A. GARCÍA

Professor

Researcher ID: B-8367-2013
Knowledge area: Matemàtica Aplicada

Research group: Sistemes dinàmics aplicats en energia solar

Contact Information
Mathematics
Escuela Politécnica Superior, Avda. Jaume II, 69
973702728
garcia(a)matematica.udl.cat

Other publications

García IA, Giné J. (2003). Problemas Resueltos de Álgebra Lineal . In Collecció Eines . Volume. 45 . (pp. 1 - 155) . Edicions de la Universitat de Lleida . ISBN: 84-8409-974-1 .
García IA. (2005). Teoría de estabilidad y control . In Col.lecció Eines . Volume. 52 . (pp. 1 - 129) . Edicions de la Universitat de Lleida . ISBN: 84-8409-923-7 .
García IA, Giné J, Sorolla J. (2003). Limit Cycles in Family (I) of Ye Yan-Qian . In Actas del XVIII C.E.D.Y.A. / VIII C.M.A. . (pp. 283 - 285) .
García IA, Giné J, Grau M. (2003). Limit sign invariance through rays of the angular speed to tackle the monodromy problem . In Actas en CD del XVIII C.E.D.Y.A / VIII Congreso de Matemática Aplicada .
García IA, Giacomini H, Giné J. (2003). Generalized Nonlinear Superposition Principles . In Actas del Equadiff 2003--International Conference on Differential Equations . (pp. 334 - 336) .
García IA, Shafer D. (2003). Limit Sets of Planar Vector Fields and the Vanishing Set of Inverse Integrating Factors . In Actas del Equadiff 2003--International Conference on Differential Equations . (pp. 337 - 339) .
Chavarriga J, García IA, Sorolla J. (2004). No Existencia de Ciclos Límite Algebraicos en la Familia (I) de la Clasificación China . In Libro de resúmenes del congreso Nolineal 2004 . (pp. 63 - 63) .
Chavarriga J, García IA, Llibre J. (2004). Ciclos Límite Algebraicos en Sistemas Cúbicos de Liénard con Rozamiento Lineal . In Libro de resúmenes del congreso Nolineal 2004 . (pp. 49 - 49) .
García IA, Giacomini H, Grau M. (2007). Ciclos Límite Algebraicos en Sistemas Cúbicos de Liénard con Rozamiento Lineal . In Libro de resúmenes del congreso Nolineal 2007 . (pp. 41 - 41) .
García IA, Giné J, Maza S. (2007). Linearización de Campos Vectoriales Suaves en el plano complejo mediante simetrías de Lie . In Libro de resúmenes del congreso Nolineal 2007 . (pp. 76 - 76) .
García IA, Giné J, Maza S. (2008). Órbitas periódicas en sistemas Newtonianos con álgebra de simetrías puntuales de Lie 2-dimensional: Aplicación a los sistemas polinomiales de Liénard . In Libro de resúmenes del congreso Nolineal 2008 . (pp. 60 - 60) . Centro Internacional de Métodos Numéricos en Ingeniería CIMNE-UPC .
García IA, Giacomini H, Grau M. (2008). Bifurcación de Hopf generalizada en campos vectoriales planos analíticos mediante inversos de factor integrante . In Libro de resúmenes del congreso Nolineal 2008 . (pp. 121 - 121) . Centro Internacional de Métodos Numéricos en Ingeniería CIMNE-UPC .
Buica A, García IA. (2009). Periodic solutions of the perturbed symmetric Euler top . In Libro de resúmenes del congreso International Workshop on Resonance Oscillations and Stability of Nonsmooth Systems . (pp. 9 - 9) .
García IA, Giacomini H, Grau M. (2009). Bifurcacition of limit cycles from some monodromic limit sets in analytic planar vector fields . In Program Equadiff 12, Conference on differential equations and their applications. Academy of sciences of the Czech Republic . (pp. 85 - 85) .
García IA, Maza M. (2009). A new approach for center conditions for simple analytic monodromic singularities . In Program Equadiff 12, Conference on differential equations and their applications. Academy of sciences of the Czech Republic . (pp. 104 - 104) .
García IA, Maza S. (2009). Métodos Numéricos:Problemas Resueltos y Prácticas . In Col.lecció Eines . Volume. 62 . (pp. 1 - 362) . Edicions de la Universitat de Lleida . ISBN: 978-84-8409-294-0 .
García IA, Giné J, Maza S (2010). Problemas Resueltos de Cálculo . In Col.lecció Eines . Volume. 69 . (pp. 1 - 153) . Edicions de la Universitat de Lleida . ISBN: 978-84-8409-379-4 .
Buica A, García IA. (2011). Bifurcation of periodic orbits from period manifolds of the Euler top . In Abstract book, International Conference on Differential and Difference Equations and Applications . (pp. 75 - 76) .
Buica A, García IA, Maza S. (2011). The center problem on smooth two-dimensional center manifolds via Jacobi last multipliers . In Abstract book, International Conference on Differential and Difference Equations and Applications . (pp. 95 - 96) .
Buica A, García IA, Maza S. (2012). El problema del centro sobre una variedad central 2-dimenional mediante inversos de multiplicadores de Jacobi . In Libro de resúmenes del congreso Nolineal 2012 . (pp. 65 - 65) .
García IA, Llibre J, Maza S. (2012). Ciclicidad de un foco simple a través de la multiplicidad de anulación de inversos de factor integrantes . In Libro de resúmenes del congreso Nolineal 2012 . (pp. 100 - 100) .
García IA, Llibre J, Maza S. (2012). Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors . In New Trends in Dynamical Systems . (pp. 48 - 49) .
García IA, Llibre J, Maza S. (2012). Periodic orbits in the Rössler prototype-4 system . In New Trends in Dynamical Systems . (pp. 58 - 59) .
García IA, Maza S. (2013). Curso de Introducción al Cálculo para Grados en Ingeniería . In Col.lecció Eines . Volume. 73 . (pp. 1 - 219) . Edicions de la Universitat de Lleida . ISBN: 978-84-8409-597-2 .
Buica A, García IA. (2013). Non-isolated T-periodic orbits of T-periodic differential equations through inverse Jacobi multipliers . In Abstracts book of Equadiff 2013 . (pp. 222 - 222) .
Buica A, García IA. (2013). Continua of T-periodic solutions of T-periodic dynamical systems . In Actas del XXIII Congreso de Ecuaciones Diferenciales y Aplicaciones XIII Congreso de Matemática Aplicada . (pp. 683 - 685) .
García IA, Maza S, Shafer D.S. (2013). Properties of monodromic points on center manifolds in R^3 via Lie symmetries . In Actas del XXIII Congreso de Ecuaciones Diferenciales y Aplicaciones XIII Congreso de Matemática Aplicada . (pp. 695 - 700) .
García IA, Maza S, Shafer D.S. (2013). Properties of monodromic points on center manifolds in R^3 via Lie symmetries . In Dynamical Systems-Applications, Editors: J. Awrejcewicz, M. Ka\'zmierczak, P. Olejnik, J. Mrozowski. . (pp. 421 - 426) .
Buica A, García IA. (2013). Continua of T-periodic solutions of T-periodic dynamical systems . In Dynamical Systems-Theory, Editors: J. Awrejcewicz, M. Ka\'zmierczak, P. Olejnik, J. Mrozowski. . (pp. 337 - 342) .
García IA, Shafer DS. (2015). Cyclicity of nilpotent centers with homogeneous nonlinearities . In Proceedings of the XXIV congress on differential equations and applications XIV congress on applied mathematics . (pp. 195 - 199) .
García I.A.; Llibre J.; Maza S. (2016). Improvements to the averaging theory of periodic differential equations . (pp. 395 - 395) .
García IA. (2018). Bautin-type analysis in 1-dimensional averaging theory for periodic differential systems . In Abstracts book of NoLineal 2018 . (pp. 1 - 1) .

Lectures

Simetrías de Lie en ecuaciones diferenciales ordinarias . (Conferencia invitada por el CRM (Centre de Recerca Matemàtica). Universidad Autónoma de Barcelona). 09/12/2002. Barcelona. SPAIN
El Problema de Poincaré y los Ciclos Límite Algebraicos . (Conferencia invitada por la Universidad Técnica Federico Santa María). 02/04/2004. Valparaiso. CHILE
The Cyclicity of some Monodromic Limit Sets in Analytic Planar Vector Fields . (Conferencia invitada por Department of Applied Mathematics, Babes-Bolyai University). 09/07/2009. Cluj-Napoca. ROMANIA

Stays abroad in Research Centers

Department of Mathematics. University of North Carolina. Charlotte. UNITED STATES. 2003 (3 Months) . Teoría geométrica de ecuaciones diferenciales con énfasis en bifurcación de ciclos límite . **Convidat - Recerca
Departamento de Matemática de la Universidad Técnica Federico Santa María. Valparaiso. CHILE. 2004 (40 Days) . El problema tangencial 16 de Hilbert en sistemas de Kukles de grado arbitrario . **Convidat - Recerca
Laboratoire de Mathématiques et Physique Théorique, Facultad de Ciencias y Técnicas de la Universidad de Tours.. Tours. FRANCE. 2005 (7 Days) . Bifurcaciones de ciclos límite en policiclos monodrómicos acotados y no degenerados. . **Convidat - Recerca
Laboratoire de Mathématiques et Physique Théorique, Facultad de Ciencias y Técnicas de la Universidad de Tours.. Tours. FRANCE. 2008 (7 Days) . Bifurcación de Hopf via inversos de factor integrante. . **Convidat - Recerca
Department of Applied Mathematics, Babes-Bolyai University. Cluj-Napoca. ROMANIA. 2009 (1 Months) . Estudio de la bifurcación de Hopf en dimensión arbitraria . **Convidat - Recerca
Laboratoire de Mathématiques et Physique Théorique, Facultad de Ciencias y Técnicas de la Universidad de Tours.. Tours. FRANCE. 2009 (7 Days) . Bifurcaciones Singulares y nversos de factor integrante. . **Convidat - Recerca
Departamento de Física de la Universidad Rey Juan Carlos.. Madrid. SPAIN. 2011 (3 Days) . Estudio de los polinomios de Darboux en sistemas de Poisson . **Convidat - Recerca
Department of Mathematics. University of North Carolina. Charlotte. UNITED STATES. 2012 (2 Months) . Simetrías de Lie aplicadas al problema del centro sobre variedades centrales . **Convidat - Recerca
Departamento de Física de la Universidad Rey Juan Carlos.. Madrid. SPAIN. 2013 (3 Days) . Estudios perturbativos en sistemas de Poisson . **Convidat - Recerca
Department of Mathematics. University of North Carolina. Charlotte. UNITED STATES. 2017 (3 Months) . Ciclicidad de puntos monodrómicos nilpotentes . **Convidat - Recerca

Academic training

Ciencias Físicas . Universidad de Barcelona . 01/02/1995 . (Diploma / Degree / Activities)
Ciencias Matemáticas . Universidad Autónoma de Barcelona . 09/06/2000 . (Ph.D.)

Activity interests

La nostra recerca s'emmarca dins el camp de la teoria qualitativa de les equacions diferencials en dimensió arbitraria amb especial èmfasi al pla, des de punts de vista tant analítics com algebraics i geomètrics. Actualment, treballo en problemes d'integrabilitat (racional, Darboux i Liouville) d'equacions diferencials polinomials, determinació de l'estabilitat de les solucions i determinació del nombre i propietats dels cicles límit i conjunts w-límit en general . Universitat de Lleida

Participations in Conferences

García IA, Giné J. (2002). Cofactores generalizados e integrales primeras no Liouville. (Communication presentation) . NoLineal 2002 . Resumenes del congreso . Cuenca . SPAIN
García IA, Giné J. (2002). Algebraic and non-algebraic invariant curves for polynomial planar vector fields. (Guest lecture) . Bifurcations de systèmes différentiels, applications à la biologie. Centre International de Rencontres Mathématiques (C.I.R.M.) . Luminy (Marsella) . FRANCE
García IA. (2003). Dynamical Applications of Continuous Groups of Symmetries for Ordinary Differential Equations. (Guest lecture) . Carolina Dynamics Meeting . Charlotte . UNITED STATES
García IA, Shafer DS. (2003). Limit Sets of Planar Vector Fields and the Vanishing Set of Inverse Integrating Factors. (Communication presentation) . Equadiff 2003- International Conference on Differential Equations . Hasselt . BELGIUM
García IA, Giné J, Grau M. (2003). Limit Sign Invariance Through Rays of the Angular Speed to Tackle the Monodromy Problem. (Communication presentation) . XVIII C.E.D.Y.A. / VIII C.M.A . Tarragona . SPAIN
García IA, Giné J, Sorolla J. (2003). Limit cycles in family (I) of Ye Yan-Quian. (Communication presentation) . XVIII C.E.D.Y.A. y VIII Congreso de Matemática Aplicada . Resumenes del Congreso y Actas en CD ROM . Tarragona . SPAIN
García IA, Giacomini H, Giné J. (2003). Generalized nonlinear superposition principle. (Guest lecture) . Families of polynomial vector fields on the plane. Centre Émile Borel, Institut Henri Poincaré . Paris . FRANCE
Chavarriga J, García IA, Llibre J. (2004). Ciclos Límite Algebraicos en Sistemas Cúbicos de Liénard con Rozamiento Lineal. (Communication presentation) . Nolineal 2004 . Libro de resúmenes del congreso Nolineal 2004. ISBN 84-688-7462-0 . Toledo . SPAIN
García IA, Shafer DS. (2006). Limit Sets of Planar Vector Fields via Integral Invariants. (Communication presentation) . Barcelona Conference on Planar Vector Fields . Barcelona . SPAIN
García IA, Giné J, Llibre J. (2006). Liénard and Riccati Differential Equations Related via Lie Algebras. (Guest lecture) . International Conference on Bifurcation Theory of Dynamical Systems and Related Topics. School of Mathematical Sciences . Pekin . CHINA
García IA, Giacomini H, Grau M. (2007). Bifurcación de Ciclos Límite de un Gráfico Compacto Monodrómico a través del Inverso de Factor Integrante. (Communication presentation) . Nolineal 2007 . Ciudad Real . SPAIN
García IA, Giné J, Maza S. (2007). Linearización de Campos Vectoriales suaves en el plano complejo mediante Simetrías de Lie. (Communication presentation) . NoLineal 2007 . Ciudad Real . SPAIN
García IA, Giacomini H, Grau M. (2007). Estudio de la Bifurcación de Ciclos Límite a partir de un Gráfico mediante el Inverso de Factor Integrante. (Communication presentation) . XX C.E.D.Y.A. / X C.M.A . Sevilla . SPAIN
García IA, Giacomini H, Grau M. (2008). Bifurcación de Hopf Generalizada en Campos Vectoriales Planos Analíticos Mediante Inversos de Factor Integrante. (Communication presentation) . NoLineal 2008 . Barcelona . SPAIN
García IA, Giné J, Maza S. (2008). No existencia de órbitas periódicas en sistemas Newtonianos con álgebra de simetrías puntuales de Lie 2-dimensional. (Communication presentation) . Workshop sobre Órbitas Periódicas de Ecuaciones Diferenciales . Tossa de Mar . SPAIN
García IA, Giacomini H, Grau M. (2008). Study of the cyclicity using the inverse integrating factor. (Guest lecture) . Classical Problems on Planar Polynomial Vector Fields . Banff . CANADA
García IA, Giacomini H, Grau M. (2009). On the cyclicity of analytic nilpotent foci. (Guest lecture) . Singularities of Planar Vector Fields, Bifurcations and Applications . Marsella . FRANCE
García IA, Giacomini H, Grau M. (2009). Bifurcation of Limit Cycles from some Monodromic Limit Sets in Analytic Planar Vector Fields. (Communication presentation) . Equaddif 12 . Brno . CZECH REPUBLIC
García IA, Giacomini H, Grau M. (2009). The Cyclicity of some Monodromic Limit Sets in Analytic Planar Vector Fields. (Guest lecture) . Ukrainian Mathematical Congress-2009 . Kyiv . UKRAINE
García IA (2010). . (Organizing committee member) . Third Symposium on Planar Vector Fields . Lleida . SPAIN
García IA (2010). . (**Sense especificar) . DDAYS 2010 . Calatayud . SPAIN
Isaac A. García (2011). . (**Sense especificar) . Advances in Qualitative Theory of Differential Equations . Castro Urdiales . SPAIN
Buica, A.; García, I.A. (2011). The perturbed symmetric Euler top and its periodic solutions. (Communication presentation) . XXII CEDYA / XII CMA . Palma de Mallorca . SPAIN
Buica, A.; García, I.A. (2011). Bifurcation of periodic orbits from period manifolds of the Euler top. (Communication presentation) . International Conference on Differential and Difference Equations and Applications . Ponta Delgada . PORTUGAL
Buica A; García IA; Maza S. (2012). Centers on center manifolds in R^3 and the vanishing set of inverse Jacobi multipliers. (Guest lecture) . Carolina Dynamics Symposium . UNITED STATES
Buica A; García IA; Maza S. (2012). El problema del centro sobre una variedad central 2-dimensional mediante inversos de multiplicadores de Jacobi. (Communication presentation) . Nolineal 2012 . Zaragoza . SPAIN
Buica A; García IA; Maza S. (2012). Centers on center manifolds and multiple Hopf bifurcations via inverse Jacobi multipliers. (Communication presentation) . Dynamical Systems: 100 years after Poincaré . Gijón . SPAIN
García IA; Llibre J; Maza S. (2012). Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors. (**Póster) . New Trends in Dynamical Systems . Salou . SPAIN
García IA; Maza S; Shafer DS. (2012). Characterizing centers on center manifolds in R^3 via Lie symmetries. (Communication presentation) . International Conference on the Theory, Methods and Applications of Nonlinear Equations . Kingsville . UNITED STATES
Isaac A. García (2013). On slow-fast dynamics: theory, numerics, application to life and earth sciences. (**Sense especificar) . Barcelona . SPAIN
Buica A.; García IA. (2013). Non-isolated T-periodic orbits of T-periodic differential equations through inverse Jacobi multipliers. (Communication presentation) . Equadiff 13 . Praga . CZECH REPUBLIC
Buica A.; García IA. (2013). Continua of T-periodic solutions for T-periodic dynamical systems. (Communication presentation) . XXIII CEDYA / XIII CMA . Castellón . SPAIN
Buica A.; García IA. (2013). Continua of T-periodic solutions for T-periodic dynamical systems. (Communication presentation) . 12th Conference on Dynamical Systems-Theory and Applications . Lodz . POLAND
García IA; Valls C. (2014). The 3-dimensional center problem for the analytic zero-Hopf singularity. (Guest lecture) . The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications . Madrid . SPAIN
Isaac A. García (2014). El problema del centro en dimensión 3. (Guest lecture) . DDAYS 2014 . Badajoz . SPAIN
García, I.A., Shafer, D.S. (2015). Ciclicidad de centros nilpotentes con nolinealidades homogéneas. (Guest lecture) . XXIV CEDYA / XIV CMA . Cádiz . SPAIN
García IA, Llibre J, Maza S. (2016). Improvements to the averaging theory of periodic differential equations. (Communication presentation) . The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications . Orlando . UNITED STATES
Isaac A. García (2017). The 3-dimensional analytic zero-Hopf singularity: center problem, integrability and normal forms. (Guest lecture) . 2017 Carolina Dynamics Symposium . UNITED STATES
García IA, Llibre J, Maza S. (2018). Bautin-type analysis in 1-dimensional averaging theory for periodic differential equations. (Communication presentation) . NoLineal 2018, International Conference on Nonlinear Mathematics and Physics . Málaga . SPAIN
García, I.A.; Maza, S.; Shafer, D.S. (2019). The center cyclicity of the Lorenz, Chen and Lü systems. (Guest lecture) . AQTDS2019 Advances in Qualitative Theory of Differential Equations . Castro Urdiales . SPAIN
García, I.A (2020). Bautin-type analysis for the cyclicity of polynomial families of three-dimensional zero-Hopf singularities. (Guest lecture) . Bifurcations and finiteness problems in ordinary differential equations . Barcelona . SPAIN

Participation in Committees and Representations

Miembro del tribunal de Tesis Doctoral (Matemática) de la alumna Maria Teresa Grau Montaña . (2004) . Contribution to the qualitative study of planar differential systems . 2004
Vocal del tribunal de Tesis Doctoral (Matemática) del alumno Jordi Sorolla Bardají . (2005) . On the algebraic limit cycles of quadratic systems . 2005
Vocal del tribunal de Tesis Doctoral (Matemática) del alumno Antonio Ferragut . (2006) . Polynomial inverse integrating factors of quadratic systems and other results . 2006
Vocal (Rapporteur) del tribunal de Tesis Doctoral (Matemática) del alumno Islam Boussaada . (2008) . Contribution à l'étude des solutions périodiques et des centres isochrones des systèmes d'équations différentielles ordinaires planes . 2008
Consejo Ejecutivo de SEMA (Sociedad Española de Matemática Aplicada) . (10/09/2016) . Vocal . 10/09/2013 - 10/09/2016
Miembro del tribunal de Tesis Doctoral (Matemática) del alumno Jackson Itikawa . (22/07/2015) . Uniform isochronous centers of degrees 3 and 4 and their perturbations . 22/07/2015
Miembro del tribunal de Tesis Doctoral (Matemática) del alumno Murilo Rodolfo Candido . (17/07/2018) . New Results in Averaging Theory and its Applications . 17/07/2018
Premio extraordinario de doctorado 2015/16 en el ámbito Informática-Matemática . (27/06/2018) . Presidente del tribunal . 27/06/2018
5a Jornada de Sistemes Dinàmics a Catalunya . (30/12/2020) . Miembro del comité científico . 01/01/2020 - 30/12/2020

Projects

Estudio cualitativo de los sistemas dinámicos con énfasis en sus bifurcaciones (Programa Nacional de Promoción General del Conocimiento - Física y Matemàticas (BFM)) . 2002 - 2005 . Ref.BFM2002-04236-C02-01 . Ministerio de Ciencia y Tecnología (MICYT) . PI: Javier Chavarriga Soriano . (3 Researchers)
Órbitas periódicas y aproximación algebraica de ciclos límite en sistemas diferenciales planos (Sense especificar) . 2002 . Ref.P01-Universitat de Lleida . Universitat de Lleida (UdL) . PI: Jaume Giné Mesa . (3 Researchers) . Convocatoria de nuevas incorporaciones y otras acciones de soporte a la investigación (Universitat de Lleida)
Convocatòria d'equipament i infraestructura destinat a la recerca (PEIR) (Material d'equipament i infraestructura destinat a la recerca) (Infraestructura de la Generalitat de Catalunya (PEIR)) . 2005 . Ref.PEIR 10020/12 . Departament d'Universitats, Recerca i Societat de la Informació (Generalitat de Catalunya) DURSI . PI: Luisa Fernanda Cabeza Fabra . (16 Researchers)
Métodos algebraicos e integrabilidad en las ecuaciones diferenciales polinomiales (Programa Nacional de Matemáticas (MTM)) . 2005 - 2008 . Ref.MTM2005-06098-C02-02/ . Ministerio de Educación y Ciencia . PI: Jaume Giné Mesa . (4 Researchers)
  • Centro
  • Género
  • Integrabilidad
  • Solución algebraica
Seminari de Sistemes Dinamics (Ajuts a la Recerca) . 2006 - 2008 . Departament d'Universitats, Recerca i Societat de la Informació (Generalitat de Catalunya) DURSI . PI: Isaac Antoni Garcia Rodriguez . (3 Researchers) . Reconeixement de grup de recerca singular (Modalitat C) per la Generalitat de Catalunya en la Resolució de 18 d'Octubre de 2005. Projecte sol.licitat en la convocatoria 2005. Sol.licitud d'Ajuts de Suport als Grups de Recerca de Catalunya (SGR) en la modalitat de Grup de Recerca Singular (GRS).
Métodos Cualitativos e Integrabilidad en las Ecuaciones Diferenciales en el Plano (Programa Nacional de Matemáticas (MTM)) . 2009 - 2011 . Ref.MTM2008-00694/MTM . Ministerio de Ciencia e Innovación . PI: Jaume Gine Mesa . (6 Researchers)
  • Género
  • Integrabilidad
  • Centro
  • Solución algebraica
Dinámica, Atractores y Nolinealidad: Caos y Estabilidad. (Acción complementaria) (Programa Nacional de Matemáticas (MTM)) . 2009 - 2010 . Ref.MTM2008-01396 -E/MTM . Ministerio de Ciencia e Innovación . PI: Carmen Nuñez Jiménez . (209 Researchers)
Dinámica, atractores y nolinealidad: caos y estabilidad (Programa Nacional de Matemáticas (MTM)) . 2008 . Ref.MTM2007-29352-E . Ministerio de Educación y Ciencia . PI: Àngel Jorba
Dinámica, Atractores y Nolinealidad: Caos y Estabilidad. (Acción complementaria) (Programa Nacional de Matemáticas (MTM)) . 2010 - 2011 . Ref.MTM2009-06507–E/MTM . Ministerio de Ciencia e Innovación . PI: Carmen Núñez Jiménez . (221 Researchers)
Bifurcaciones, integrabilidad y propiedades cualitativas de familias de campos vectoriales (Programa Nacional de Promoción General del Conocimiento - Física y Matemàticas (BFM)) . 2012 - 2014 . Ref.MTM2011-22877 . Ministerio de Ciencia e Innovación . PI: Isaac Antonio García Rodríguez . (6 Researchers)
Servei d'automatització per al tractament intel.ligent d'imatges de satèl.lit (Contracte de recerca) . 2020 - 2021 . Ref.C20038 . VUNKERS IT EXPERTS, S.L.U . PI: Carlos J. Ansotegui Gil . (5 Researchers)
Calibrado inteligente de algoritmos para COVID19 (CAINALCO) (Ajuts a la Recerca) . 2020 - 2021 . CSIC-Santander . PI: Carlos J. Ansotegui Gil

Journal Publications

García IA, Giné J. (2003). Generalized cofactors and nonlinear superposition principles. Applied Mathematics Letters, 16(7), pp. 1137 - 1141 . ISSN: 0893-9659
Chavarriga J, García IA. (2003). Some criteria for the existence and uniqueness of limit cycles for quadratic vector fields. Journal of Mathematical Analysis and Applications(282), pp. 296 - 304 . ISSN: 0022-247X
García IA. (2003). On the integrability of quasihomogeneous and related planar vector fields. International Journal of Bifurcation and Chaos, 13(4), pp. 995 - 1002 . ISSN: 0218-1274
García IA, Giné J. (2004). Non-algebraic invariant curves for polynomial planar vector fields. Discrete and Continuous Dynamical Systems, 10(3), pp. 755 - 768 . ISSN: 1078-0947
García IA, Giacomini H, Giné J. (2005). Generalized Nonlinear Superposition Principles for Polynomial Planar Vector Fields. Journal of Lie Theory, 24(2), pp. 491 - 499 . ISSN: 0949-5932
Chavarriga J, García IA. (2005). Lie Symmetries of quasihomogeneous polynomial planar vector fields and certain perturbations. Acta Mathematica Sinica-English Series, 21(1), pp. 185 - 192 . ISSN: 1439-8516
García IA, Giné J, Sorolla J. (2005). On the Existence of Polynomial Inverse Integrating Factors in Quadratic Systems with Limit Cycles. Dynamics of Continuous Discrete and Impulsive Systems, 12(2), pp. 151 - 174 . ISSN: 1201-3390
García IA, Shafer DS. (2005). Integral invariants and limit sets of planar vector fields. Journal of Differential Equations, 217, pp. 363 - 376 . ISSN: 0022-0396
García IA. (2005). Transcendental Limit Cycles via the Structure of Arbitrary Degree Invariant Algebraic Curves of Polynomial Planar Vector Fields. Rocky Mountain Journal of Mathematics, 35(2), pp. 501 - 515 . ISSN: 0035-7596
Chavarriga J, García IA, Sorolla J. (2005). Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of chinese classification. Chaos Solitons & Fractals, 24(2), pp. 491 - 499 . ISSN: 0960-0779
Chavarriga J, García IA. (2006). Existence of limit cycles for real quadratic differential systems with an invariant cubic. Pacific Journal of Mathematics, 223(2), pp. 201 - 218 . ISSN: 0030-8730
Chavarriga J, García IA, Sorolla, J. (2006). Non-nested configuration of algebraic limit cycles in quadratic systems. Journal of Differential Equations, 225(2), pp. 513 - 527 . ISSN: 0022-0396
Chavarriga J, García IA. (2006). The Poincaré Problem in the Non-Resonant Case: An Algebraic Approach. Differential Geometry Dynamical Systems, 8, pp. 54 - 68 . ISSN: 1454-511X
García IA, Giné J, Grau M. (2006). A Necessary Condition in the Monodromy Problem for Analytic Differential Equations on the Plane. Journal of Symbolic Computation, 41(9), pp. 943 - 958 . ISSN: 0747-7171
Chavarriga J, García IA, Llibre J, Zoladek H. (2006). Invariant algebraic curves for the cubic Lienard system with linear damping. Bulletin des Sciences Mathematiques, 130(5), pp. 428 - 441 . ISSN: 0007-4497
Chavarriga J, García IA, Sáez E, Szántó I. (2007). Limit Cycles in Kukles Systems of Arbitrary Degree with Invariant Ellipse. Nonlinear Analysis-Theory Methods & Applications, 67(4), pp. 1005 - 1014 . ISSN: 0362-546X
García IA, Giné J, Llibre J. (2008). Liénard and Riccati Differential Equations Related via Lie Algebras. Discrete and Continuous Dynamical Systems-Series B, 10(2 & 3), pp. 485 - 494 . ISSN: 1531-3492
García IA, Maza S. (2008). Linearization of analytic isochronous centers from a given commutator. Journal of Mathematical Analysis and Applications, 339(1), pp. 740 - 745 . ISSN: 0022-247X
García IA, Giné J, Maza S. (2008). Linearization of Smooth Planar Vector Fields around Singular Points via Commuting Flows. Communications On Pure And Applied Analysis, 7(6), pp. 1415 - 1428 . ISSN: 1534-0392
Garcia IA, Giacomini H, Grau M (2010). The inverse integrating factor and the Poincaré map. Transactions of the American Mathematical Society, 362, pp. 3591 - 3612 . Institutional Repository . ISSN: 0002-9947
García IA, Giné J. (2009). The Center Problem via Averaging Method. Journal of Mathematical Analysis and Applications, 351, pp. 334 - 339 . ISSN: 0022-247X
García IA, Maza, S. (2010). A New Approach to Center Conditions for Simple Analytic Monodromic Singularities. Journal of Differential Equations, 248, pp. 363 - 380 . ISSN: 0022-0396
García IA, Giné J. (2010). Analytic Nilpotent Centers with Analytic First Integral. Nonlinear Analysis-Theory Methods & Applications, 72, pp. 3732 - 3738 . ISSN: 0362-546X
Garcia IA; Grau M (2010). A survey on the inverse integrating factor. Qualitative Theory Of Dynamical Systems, 9(1), pp. 115 - 166 . Institutional Repository . ISSN: 1575-5460
García IA, Hernández-Bermejo B. (2010). Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces. Physica D, 239, pp. 1665 - 1669 . ISSN: 0167-2789
García IA, Giné J, Maza S. (2010). Periodic Solutions of Second-Order Differential Equations with Two-Dimensional Lie Point Symmetry Algebra. Nonlinear Analysis-Real World Applications, 11, pp. 4128 - 4140 . ISSN: 1468-1218
Buica A, García IA. (2010). Periodic solutions of the perturbed symmetric Euler top. Topological Methods In Nonlinear Analysis, 36, pp. 91 - 100 . ISSN: 1230-3429
Garcia IA; Grau M; Llibre J (2010). First integrals and Darboux polynomials of natural polynomial Hamiltonian systems. Physics Letters A, 374, pp. 4746 - 4748 . ISSN: 0375-9601
García IA, Giacomini H, Grau M. (2011). Generalized Hopf Bifurcation for Planar Vector Fields via the Inverse Integrating Factor. Journal Of Dynamics And Differential Equations, 23, pp. 251 - 281 . ISSN: 1040-7294
Buica A, García IA, Maza, S. (2012). Existence of inverse Jacobi multipliers around Hopf points in R^3: emphasis on the center problem. Journal of Differential Equations, 252(12), pp. 6324 - 6336 . https://doi.org/10.1016/j.jde.2012.03.009 . ISSN: 0022-0396
García IA. (2013). Orbital linearization around equilibriums of vector fields in R^n and Lie symmetries. Journal of Mathematical Analysis and Applications, 405, pp. 111 - 115 . ISSN: 0022-247X
García IA, Hernandez-Bermejo B. (2013). Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces. Bulletin des Sciences Mathematiques, 137(3), pp. 242 - 250 . https://doi.org/10.1016/j.bulsci.2011.09.005 . ISSN: 0007-4497
Garcia IA, Llibre J, Maza S. (2013). Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors. Journal of Differential Equations, 255(1), pp. 388080 - 3896 . Institutional Repository . ISSN: 0022-0396
Buica A, García IA, Maza, S. (2014). Multiple Hopf bifurcation in R^3 and inverse Jacobi multipliers. Journal of Differential Equations, 252(256), pp. 310 - 325 . https://doi.org/10.1016/j.jde.2013.09.006 . ISSN: 0022-0396
García IA, Maza S, Shafer DS. (2013). Properties of Monodromic Points on Center Manifolds in via Lie Symmetries. Journal Of Dynamics And Differential Equations, 25(4), pp. 981 - 1000 . https://doi.org/10.1007/s10884-013-9326-1 . ISSN: 1040-7294
Buica A, García IA, Maza S. (2013). Inverse Jacobi multipliers: recent applications in dynamical systems. Springer Proceedings in Mathematics, 54, pp. 127 - 141 . https://doi.org/10.1007/978-3-642-38830-9_8 . ISSN: 2190-5614
Buica A, García IA, Maza S. (2013). Centers in a quadratic system obtained from a scalar third order differential equation. Springer Proceedings in Mathematics, 47, pp. 405 - 410 . https://doi.org/10.1007/978-1-4614-7333-6_34 . ISSN: 2190-5614
Garcia IA; Llibre J; Maza S. (2014). On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables. Applied Mathematics and Computation, 232(1), pp. 84 - 90 . Institutional Repository . ISSN: 0096-3003
García IA, Hernández-Bermejo B. (2014). Periodic orbits in analytically perturbed Poisson systems. Physica D, 276, pp. 1 - 6 . ISSN: 0167-2789
García IA, Maza S. (2014). Linearization of nondegenerate analytic centers in R^3. Dynamical Systems-An International Journal, 29, pp. 98 - 105 . ISSN: 1468-9367
Buica A, García IA, Maza S. (2014). Some remarks on inverse Jacobi multipliers around Hopf singularities. Journal of Mathematical Analysis and Applications, 418(2), pp. 1074 - 1083 . https://doi.org/10.1016/j.jmaa.2014.04.034 . ISSN: 0022-247X
García IA (2015). Complete integrability, orbital linearizability and independent normalizers for local vector fields in R^n. Journal of Lie Theory, 25, pp. 37 - 43 . Institutional Repository . ISSN: 0949-5932
Isaac A. García (2014). Dynamical Days 2014. Boletin electrónico SeMA, 5, pp. 18 - 18 . ISSN: 1575-9822
García IA, Llibre J, Maza, S. (2015). The Hopf cyclicity of the centers of a class of quintic polynomial vector fields. Journal of Differential Equations, 258, pp. 1990 - 2009 . Institutional Repository . ISSN: 0022-0396
Buica A, García IA. (2015). Inverse Jacobi multipliers and first integrals for nonautonomous differential systems. Zeitschrift für Angewandte Mathematik und Physik, 66, pp. 573 - 585 . Institutional Repository . ISSN: 0044-2275
García IA. (2016). The cyclicity of polynomial centers via the reduced Bautin depth. Proceedings of the American Mathematical Society, 144, pp. 2473 - 2478 . Institutional Repository . ISSN: 0002-9939
García IA; Valls C. (2016). The three-dimensional center problem for the zero-Hopf singularity. Discrete and Continuous Dynamical Systems, 36(4), pp. 2027 - 2046 . Institutional Repository . ISSN: 1078-0947
García IA; Shafer DS. (2016). Cyclicity of a class of polynomial nilpotent center singularities. Discrete and Continuous Dynamical Systems, 36(5), pp. 2497 - 2520 . Institutional Repository . ISSN: 1078-0947
García IA. (2016). Cyclicity of some symmetric nilpotent centers. Journal of Differential Equations, 260(6), pp. 5356 - 5377 . Institutional Repository . ISSN: 0022-0396
García IA. (2016). Formal inverse integrating factors and the nilpotent center problem. International Journal of Bifurcation and Chaos, 26, pp. 10 - 13 . Institutional Repository . ISSN: 0218-1274
García IA, Giacomini H, Giné J, Llibre J. (2016). Analytic nilpotent centers as limits of nondegenerate centers revisited. Journal of Mathematical Analysis and Applications, 441(2), pp. 893 - 899 . Institutional Repository . ISSN: 0022-247X
Garcia IA, Llibre J, Maza S. (2016). Center cyclicity of a family of quartic polynomial differential system. Nodea-Nonlinear Differential Equations and Applications, 23(3), pp. 1 - 10 . Institutional Repository . ISSN: 1021-9722
García IA. (2016). Non-smooth quadratic centers defined in two arbitrary sectors. Applied Mathematics and Computation, 289, pp. 37 - 47 . Institutional Repository . ISSN: 0096-3003
García IA. (2018). Integrable zero-Hopf singularities and 3-dimensional centers. Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 148, pp. 327 - 340 . Institutional Repository . ISSN: 0308-2105
Garcia, IA.; Valls, C. (2018). Zero-Hopf polynomial centers of third-order differential equations. Journal Of Dynamics And Differential Equations, 30, pp. 557 - 578 . Institutional Repository . ISSN: 1040-7294
García IA. (2017). Examples of center cyclicity bounds using the reduced Bautin depth. Proceedings of the American Mathematical Society, 145, pp. 4363 - 4370 . Institutional Repository . ISSN: 0002-9939
Garcia IA, Llibre J. (2017). Classical planar algebraic curves realizable by quadratic polynomial differential systems. International Journal of Bifurcation and Chaos, 27, pp. 1 - 12 . Institutional Repository . ISSN: 0218-1274
Garcia IA, Hernández, B. (2017). Inverse Jacobi multiplier as a link between conservative systems and Poisson structures. Journal Of Physics a-Mathematical And Theoretical, 50, pp. 1 - 17 . Institutional Repository . ISSN: 1751-8113
García IA; Maza S; Shafer D.S. (2018). Cyclicity of polynomial nondegenerate centers on center manifolds. Journal of Differential Equations, 265, pp. 5767 - 5808 . Institutional Repository . ISSN: 0022-0396
García IA; Libre J; Maza S. (2018). On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations. Nonlinearity, 31, pp. 2666 - 2688 . Institutional Repository . ISSN: 0951-7715
García IA; Maza S. (2019). Period annulus of the harmonic oscillator with zero cyclicity under perturbations with a homogeneous polynomial field. Electronic Journal Of Qualitative Theory Of Differential Equations, 3, pp. 1 - 6 . Institutional Repository . ISSN: 1417-3875
García, I.A. (2019). Cyclicity of Nilpotent Centers with Minimum Andreev Number. Eur. J. Math., 5, pp. 1293 - 1330 . Institutional Repository . ISSN: 2199-675X
García, I.A.; Maza, S.; Shafer, D.S. (2019). Center cyclicity of Lorenz, Chen and Lü systems. Nonlinear Analysis-Theory Methods & Applications, 188, pp. 362 - 376 . Institutional Repository . ISSN: 0362-546X
García, I.A.; Hernández-Bermejo, B. (2020). Perturbed rank 2 Poisson systems and periodic orbits on Casimir invariant manifolds. Journal of Nonlinear Mathematical Physics, 27(2), pp. 295 - 307 . Institutional Repository . ISSN: 1402-9251
García, I.A.; Giné, J.; Llibre, J.; Maza, S. (2021). Vanishing set of inverse Jacobi multipliers and attractor/repeller sets. Chaos, 31 . Institutional Repository . ISSN: 1054-1500
García, I.A. (2021). Center problem and nu-cyclicity of polynomial zero-Hopf singularities with non-singular rotation axis. Journal of Differential Equations, 295, pp. 113 - 137 . Institutional Repository . ISSN: 0022-0396
García, I.A. (2021). Some remarks on global analytic planar vector fields possessing an invariant analytic set. Dynamical Systems-An International Journal, 36(2), pp. 204 - 211 . Institutional Repository . ISSN: 1468-9367
García, I.A. (2021). Center cyclicity for some nilpotent singularities including the Z2-equivariant class. Communications in Contemporary Mathematics, 23, pp. 2050053-1 - 2050053-39 . Institutional Repository . ISSN: 0219-1997
García, I.A.; Giné, J. (2022). Center problem with characteristic directions and inverse integrating factors. Communications In Nonlinear Science And Numerical Simulation . ISSN: 1007-5704

Thesis, minor thesis and research reports

Carles Hernández Camisón . (2007) . Control de Trajectòries Òptimes en Vehicles Submarins (Project at end of engineering degree) . Universidad de Lleida.
Hernández Bermejo, Benito . (2008) . The Jacobi identities for finite-dimensional Poisson structures: a P.D.E. based analysis of some new constructive results and solution families (International Ph.D thesis) . Universidad de LleidaIsaac A.