Polynomial slow-fast systems on the Poincar\'e-Lyapunov sphere
| Autor: | Perez, Otavio Henrique, da Silva, Paulo Ricardo |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 Poincar\'e-Lyapunov sphere for slow-fast systems defined in $\mathbb{R}^{n}$. For the planar case, we prove a global version of the Fenichel Theorem, which assures the persistence of invariant manifolds in the whole Poincar\'e-Lyapunov disk. We also discuss the appearence of non normally hyperbolic points at infinity, namely: fold, transcritical and pitchfork singularities. Comment: 28 pages, 12 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|