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    Authors: Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume;

    Altres ajuts: Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276) In this paper we define when a polynomial differential system is orbitally universal and we show the relevance of this notion in the classical center problem, i.e. in the problem of distinguishing between a focus and a center.

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    Nonlinear Analysis
    Article . 2020 . Peer-reviewed
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      Nonlinear Analysis
      Article . 2020 . Peer-reviewed
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    Authors: Algaba Durán, Antonio; García García, Cristóbal; Reyes Columé, Manuel; Giné, Jaume;

    The first three authors are partially supported by Ministerio de Economia y Competitividad, Plan Nacional I +D+I co-financed with FEDER funds, in the frame of the project PGC2018-096265-B-I00, and by Consejería de Educación y Ciencia de la Junta de Andalucía (FQM-276, P12-FQM-1658, UHU126150 and P20 00764). The last author is partially supported by the Agencia Estatal de Investigación, Spain grant PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2021SGR 01618. For perturbations of integrable non-Hamiltonian quasi-homogeneous planar vector field whose origin is a non-degenerate singular point, orbital linearization and analytic integrability are equivalent. We show a class of analytically integrable vector fields whose origin is a degenerate singular point which is orbitally equivalent to a semi-quasi-homogeneous system, that is, it is not orbital equivalent to its lowest-degree quasi-homogeneous term. Departamento de Matemáticas

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    Nonlinear Analysis
    Article . 2023 . Peer-reviewed
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      Nonlinear Analysis
      Article . 2023 . Peer-reviewed
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    Authors: Antonio Algaba; Cristóbal García; Jaume Giné;

    In this work it is solved the analytic integrability problem around a nilpotent singularity of a differential system in the plane under generic conditions.

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    arXiv.org e-Print Archive
    Preprint . Other literature type . 2018
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    Journal of Differential Equations
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    Repositori Obert UdL
    Article . 2019
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    Journal of Differential Equations
    Article . 2019 . Peer-reviewed
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    https://doi.org/10.48550/arxiv...
    Article . 2018
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      Preprint . Other literature type . 2018
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      Journal of Differential Equations
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      Repositori Obert UdL
      Article . 2019
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      Journal of Differential Equations
      Article . 2019 . Peer-reviewed
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      Article . 2018
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    Authors: Algaba Durán, Antonio; García García, Cristóbal; Giné, Jaume;

    The authors are grateful to the referees for their valuable remarks which helped to improve the manuscript. The first and second authors are supported by a MINECO/FEDER grant number MTM2010-20907-C02-02 and by the Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658; TIC-130 and FQM-276). The third author is partially supported by a MINECO/FEDER grant number MTM2011-22877 and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate center problem. This classification can be done using the formal normal form theory and knowing a suitable normal form of any differential systems associated to each family. Departamento de Matemáticas

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    Acta Applicandae Mathematicae
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    Authors: Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume;

    Recently, in [9] is characterized the analytic integrability problem around a nilpotent singularity for differential systems in the plane under generic conditions. In this work we solve the remaining case completing the analytic integrability problem for such singularity. The first, second and third authors are partially supported by a MINECO/ FEDER grant number MTM2014-56272-C2-2 and by the Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276). The fourth author is partially supported by a MINECO/ FEDER grant number MTM2017-84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR-1276.

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    Communications on Pure & Applied Analysis
    Article . 2020 . Peer-reviewed
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      Communications on Pure & Applied Analysis
      Article . 2020 . Peer-reviewed
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    Authors: Algaba Durán, Antonio; García García, Cristóbal; Giné, Jaume;

    In this work is characterized the analytic integrability problem around a nilpotent singularity for differential systems in the plane under generic conditions. The analytic integrability problem is characterized via the existence of a formal inverse integrating factor. The relation between the analytic integrability and the existence of an algebraic inverse integrating factor is also given. The first and second authors are partially supported by a MINECO/FEDER grant number MTM2014-56272-C2-2 and by the Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276). The third author is partially supported by a MINECO/FEDER grant number MTM2017-84383-P and by an AGAUR (Generalitat de Catalunya) grant number 2017SRG 1276.

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    Repositori Obert UdL
    Article . 2019
    License: CC BY NC ND
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      Repositori Obert UdL
      Article . 2019
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    Authors: Algaba Durán, Antonio; García García, Cristóbal; Giné, Jaume;

    We consider the two-dimensional autonomous systems of differential equations where the origin is a monodromic degenerate singular point, i.e., with null linear part. In this work we give two heuristic procedures to obtain some center conditions (perhaps not necessary) for certain degenerate centers at the origin although they have characteristic directions.(c) 2023 The Authors. Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation The first two authors are partially supported by Ministerio de Economia y Competitividad, Plan Nacional I+D+I co-financed with FEDER funds, in the frameof theproject PGC2018-096265-B-I00, and by Consejería de Educación y Ciencia de la Junta de Andalucía (FQM-276,P12-FQM-1658,UHU126150andP2000764).The author is partially supported by the Agencia Estatal de Investigación grant PID2020-113758GB-I00andanAGAUR (Generalitat de Catalunya) grant number2021SGR01618 Departamento de Matemáticas

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    Authors: Algaba, Antonio; García, Cristóbal; Giné, Jaume;

    In this paper, we use a geometric criterium based on the classical method of the construction of Lyapunov functions to determine if a differential system has a focus or a center at a singular point. This criterium is proved to be useful for several examples studied in previous works with other more specific methods.

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    Mediterranean Journal of Mathematics
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    Mediterranean Journal of Mathematics; Repositori Obert UdL
    Article . 2015 . 2016 . Peer-reviewed
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      Mediterranean Journal of Mathematics
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      Mediterranean Journal of Mathematics; Repositori Obert UdL
      Article . 2015 . 2016 . Peer-reviewed
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    Authors: Algaba Durán, Antonio; Checa Camacho, Isabel; García García, Cristóbal; Giné, Jaume;

    In this paper we study the analytic integrability around the origin inside a family of degenerate centers or perturbations of them. For this family analytic integrability does not imply formal orbital equivalence to a Hamiltonian system. It is shown how difficult is the integrability problem even inside this simple family of degenerate centers or perturbations of them. The first and third authors are supported by a MINECO/FEDER grant number MTM2010-20907-C02-02 and by the Consejer´ıa de Educaci´on y Ciencia de la Junta de Andaluc´ıa (projects P12-FQM-1658, FQM-276). The fourth author is partially supported by a MINECO/FEDER grant number MTM2011-22877 and by a AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. Departamento de Matemáticas

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    Repositori Obert UdL
    Article . 2016
    License: CC BY NC ND
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    Nonlinear Analysis Real World Applications
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      Repositori Obert UdL
      Article . 2016
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      Nonlinear Analysis Real World Applications
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    Authors: Algaba Durán, Antonio; García García, Cristóbal, Matemático; Reyes Columé, Manuel;

    We characterize, using normal forms of quasi-homogeneous expansions, the analytic vector fields at nilpotent singular point having an algebraic first integral over the ring C [[ x, y ]] . As a consequence, we provide a link between the algebraic integrability problem and the existence of a formal inverse integrat- ing factor which is null at the singular point. This work has been partially supported by Ministerio de Ciencia, Innovación y Universidades, Spain (project PGC2018-096265-BI00) and by Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía, Spain (projects FQM-276, UHU-1260150 and P12-FQM-1658 Funding for open access charge: Universidad de Huelva / CBUA. Departamento de Matemáticas

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    Chaos Solitons & Fractals
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      Chaos Solitons & Fractals
      Article
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25 Research products for P12-FQM-1658
  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume;

    Altres ajuts: Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276) In this paper we define when a polynomial differential system is orbitally universal and we show the relevance of this notion in the classical center problem, i.e. in the problem of distinguishing between a focus and a center.

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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    Nonlinear Analysis
    Article . 2020 . Peer-reviewed
    License: Elsevier TDM
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Recolector de Cienci...arrow_drop_down
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
      Nonlinear Analysis
      Article . 2020 . Peer-reviewed
      License: Elsevier TDM
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Algaba Durán, Antonio; García García, Cristóbal; Reyes Columé, Manuel; Giné, Jaume;

    The first three authors are partially supported by Ministerio de Economia y Competitividad, Plan Nacional I +D+I co-financed with FEDER funds, in the frame of the project PGC2018-096265-B-I00, and by Consejería de Educación y Ciencia de la Junta de Andalucía (FQM-276, P12-FQM-1658, UHU126150 and P20 00764). The last author is partially supported by the Agencia Estatal de Investigación, Spain grant PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2021SGR 01618. For perturbations of integrable non-Hamiltonian quasi-homogeneous planar vector field whose origin is a non-degenerate singular point, orbital linearization and analytic integrability are equivalent. We show a class of analytically integrable vector fields whose origin is a degenerate singular point which is orbitally equivalent to a semi-quasi-homogeneous system, that is, it is not orbital equivalent to its lowest-degree quasi-homogeneous term. Departamento de Matemáticas

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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Nonlinear Analysis
    Article . 2023 . Peer-reviewed
    License: CC BY NC ND
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      Nonlinear Analysis
      Article . 2023 . Peer-reviewed
      License: CC BY NC ND
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      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Antonio Algaba; Cristóbal García; Jaume Giné;

    In this work it is solved the analytic integrability problem around a nilpotent singularity of a differential system in the plane under generic conditions.

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    arXiv.org e-Print Archive
    Preprint . Other literature type . 2018
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    Journal of Differential Equations
    Article
    License: CC BY NC ND
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    Repositori Obert UdL
    Article . 2019
    License: CC BY NC ND
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    Journal of Differential Equations
    Article . 2019 . Peer-reviewed
    License: Elsevier Non-Commercial
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    https://doi.org/10.48550/arxiv...
    Article . 2018
    License: arXiv Non-Exclusive Distribution
    Data sources: Datacite