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

  • Identification data

    Identifier: imarina:6466319
    Handle: https://hdl.handle.net/20.500.11797/imarina6466319
    Authors:
    Marín DVilladelprat J
    Abstract:
    © 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.

  • Others:

    Author, as appears in the article.: Marín D; Villadelprat J
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Villadelprat Yagüe, Jordi
    Keywords: Uniform flatness Period Families Dulac time Dulac map Asymptotic expansion
    Abstract: © 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.
    Thematic Areas: Mathematics Matemática / probabilidade e estatística Interdisciplinar Engenharias iii Ciências agrárias i Ciência da computação Astronomia / física Applied mathematics Analysis
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 0022-0396
    Author's mail: jordi.villadelprat@urv.cat
    Author identifier: 0000-0002-1168-9750
    Record's date: 2023-02-19
    Papper version: info:eu-repo/semantics/acceptedVersion
    Link to the original source: https://www.sciencedirect.com/science/article/abs/pii/S0022039620303387?via%3Dihub
    Papper original source: Journal Of Differential Equations. 269 (10): 8425-8467
    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
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.1016/j.jde.2020.06.024
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2020
    Publication Type: Journal Publications

  • Keywords:

    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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