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Articles 2 records found  
1.
34 p, 670.9 KB Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles : Local setting / Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
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. [...]
2020 - 10.1016/j.jde.2020.06.024
Journal of differential equations, Vol. 269, Issue 10 (November 2020) , p. 8425-8467  
Detailed record - Creative Commons
2.
38 p, 790.4 KB Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles : General setting / Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
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. [...]
2021 - 10.1016/j.jde.2020.11.020
Journal of differential equations, Vol. 275 (February 2021) , p. 684-732  
Detailed record - Creative Commons

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