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

  • Datos identificativos

    Identificador: imarina:6466319
    Handle: https://hdl.handle.net/20.500.11797/imarina6466319
    Autores:
    Marín DVilladelprat J
    Resumen:
    © 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.

  • Otros:

    Autor según el artículo: Marín D; Villadelprat J
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Villadelprat Yagüe, Jordi
    Palabras clave: Uniform flatness Period Families Dulac time Dulac map Asymptotic expansion
    Resumen: © 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.
    Áreas temáticas: Mathematics Matemática / probabilidade e estatística Interdisciplinar Engenharias iii Ciências agrárias i Ciência da computação Astronomia / física Applied mathematics Analysis
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 0022-0396
    Direcció de correo del autor: jordi.villadelprat@urv.cat
    Identificador del autor: 0000-0002-1168-9750
    Fecha de alta del registro: 2023-02-19
    Versión del articulo depositado: info:eu-repo/semantics/acceptedVersion
    Enlace a la fuente original: https://www.sciencedirect.com/science/article/abs/pii/S0022039620303387?via%3Dihub
    Referencia al articulo segun fuente origial: Journal Of Differential Equations. 269 (10): 8425-8467
    Referencia 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 Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI del artículo: 10.1016/j.jde.2020.06.024
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2020
    Tipo de publicación: Journal Publications

  • Palabras clave:

    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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