Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity at infinity of the Poincaré–Lyapunov sphere for slow-fast systems defined in Rn. For the planar case, we prove a global...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/299973 |
| Acceso en línea: | http://dx.doi.org/10.1007/s40863-024-00441-8 https://hdl.handle.net/11449/299973 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometric singular perturbation theory Invariant manifolds Poincaré compactification Poincaré–Lyapunov compactification Polynomial vector fields |
| Sumario: | The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity at infinity of the Poincaré–Lyapunov sphere for slow-fast systems defined in Rn. For the planar case, we prove a global version of the Fenichel Theorem, which assures the persistence of invariant manifolds in the whole Poincaré–Lyapunov disk. We also discuss the occurrence of non normally hyperbolic points at infinity, namely: fold, transcritical and pitchfork singularities. |
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