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Bibliographic Details
Main Authors: Perez, Otavio Henrique, da Silva, Paulo Ricardo
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.06239
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Table of Contents:
  • 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 $\mathbb{R}^{n}$. For the planar case, we prove a global version of the Fenichel Theorem, which assures the persistence of invariant manifolds in the whole Poincaré-Lyapunov disk. We also discuss the appearence of non normally hyperbolic points at infinity, namely: fold, transcritical and pitchfork singularities.