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

Given a C∞ family of planar vector fields{Xˆ µ}ˆ µ∈ ˆ W having a hyperbolic saddle, we study the Dulac map D(s; ˆ µ) and the Dulac time T(s; ˆ µ) between two transverse sections located in these paratrices at arbitrary distance from the saddle. We show (Theorems A and B, respectively) that, for any...

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Detalles Bibliográficos
Autores: Marín, David|||0000-0003-4422-6418, Villadelprat Yagüe, Jordi|||0000-0002-1168-9750
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:236661
Acceso en línea:https://ddd.uab.cat/record/236661
https://dx.doi.org/urn:doi:10.1016/j.jde.2020.11.020
Access Level:acceso abierto
Palabra clave:Dulac map
Dulac time
Asymptotic expansion
Uniform flatness
Criticality
Descripción
Sumario:Given a C∞ family of planar vector fields{Xˆ µ}ˆ µ∈ ˆ W having a hyperbolic saddle, we study the Dulac map D(s; ˆ µ) and the Dulac time T(s; ˆ µ) between two transverse sections located in these paratrices at arbitrary distance from the saddle. We show (Theorems A and B, respectively) that, for any ˆ µ0 ∈ ˆ W and L.