Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (II): The generic case
| Autor: | O. Castejón, Tere M. Seara, Inmaculada Baldomá |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Differential equations
Singular perturbation Dynamical Systems (math.DS) Hopf-zero bifurcation Equacions diferencials 01 natural sciences Singularity Exponentially small splitting FOS: Mathematics Differentiable dynamical systems Asymptotic formula Mathematics - Dynamical Systems 0101 mathematics Mathematical physics Physics Stokes constant Applied Mathematics Inner equation 010102 general mathematics General Engineering Zero (complex analysis) Matemàtiques i estadística [Àrees temàtiques de la UPC] Sistemes dinàmics diferenciables Connection (mathematics) 010101 applied mathematics 37 Dynamical systems and ergodic theory [Classificació AMS] Modeling and Simulation Vector field 35 Partial differential equations [Classificació AMS] |
| Zdroj: | Recercat. Dipósit de la Recerca de Catalunya instname UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | In this paper, we prove the breakdown of the two-dimensional stable and unstable manifolds associated to two saddle-focus points which appear in the unfoldings of the Hopf-zero singularity. The method consists in obtaining an asymptotic formula for the difference between these manifolds which turns to be exponentially small respect to the unfolding parameter. The formula obtained is explicit but depends on the so-called Stokes constants, which arise in the study of the original vector field and which corresponds to the so-called inner equation in singular perturbation theory. |
| Databáze: | OpenAIRE |
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