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
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/
Entity: Universitat Rovira i Virgili
Journal publication year: 2020
Publication Type: Journal Publications
Repositori URV