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Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: Local setting

  • Dades identificatives

    Identificador: imarina:6466319
    Handle: https://hdl.handle.net/20.500.11797/imarina6466319
    Autors:
    Marín DVilladelprat J
    Resum:
    © 2020 Elsevier Inc. In this paper we study unfoldings of planar vector fields in a neighbourhood of a hyperbolic resonant saddle. We give a structure theorem for the asymptotic expansion of the local Dulac time (as well as the local Dulac map) with the remainder uniformly flat with respect to the unfolding parameters. Here local means close enough to the saddle in order that the normalizing coordinates provided by a suitable normal form can be used. The principal part of the asymptotic expansion is given in a monomial scale containing a deformation of the logarithm, the so-called Roussarie-Ecalle compensator. Especial attention is paid to the remainder's properties concerning the derivation with respect to the unfolding parameters.

  • Altres:

    Autor segons l'article: Marín D; Villadelprat J
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Villadelprat Yagüe, Jordi
    Paraules clau: Uniform flatness Period Families Dulac time Dulac map Asymptotic expansion
    Resum: © 2020 Elsevier Inc. In this paper we study unfoldings of planar vector fields in a neighbourhood of a hyperbolic resonant saddle. We give a structure theorem for the asymptotic expansion of the local Dulac time (as well as the local Dulac map) with the remainder uniformly flat with respect to the unfolding parameters. Here local means close enough to the saddle in order that the normalizing coordinates provided by a suitable normal form can be used. The principal part of the asymptotic expansion is given in a monomial scale containing a deformation of the logarithm, the so-called Roussarie-Ecalle compensator. Especial attention is paid to the remainder's properties concerning the derivation with respect to the unfolding parameters.
    Àrees temàtiques: Mathematics Matemática / probabilidade e estatística Interdisciplinar Engenharias iii Ciências agrárias i Ciência da computação Astronomia / física Applied mathematics Analysis
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 0022-0396
    Adreça de correu electrònic de l'autor: jordi.villadelprat@urv.cat
    Identificador de l'autor: 0000-0002-1168-9750
    Data d'alta del registre: 2023-02-19
    Versió de l'article dipositat: info:eu-repo/semantics/acceptedVersion
    Enllaç font original: https://www.sciencedirect.com/science/article/abs/pii/S0022039620303387?via%3Dihub
    Referència a l'article segons font original: Journal Of Differential Equations. 269 (10): 8425-8467
    Referència de l'ítem segons les normes APA: Marín D; Villadelprat J (2020). Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: Local setting. Journal Of Differential Equations, 269(10), 8425-8467. DOI: 10.1016/j.jde.2020.06.024
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI de l'article: 10.1016/j.jde.2020.06.024
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2020
    Tipus de publicació: Journal Publications

  • Paraules clau:

    Analysis,Applied Mathematics,Mathematics
    Uniform flatness
    Period
    Families
    Dulac time
    Dulac map
    Asymptotic expansion
    Mathematics
    Matemática / probabilidade e estatística
    Interdisciplinar
    Engenharias iii
    Ciências agrárias i
    Ciência da computação
    Astronomia / física
    Applied mathematics
    Analysis

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