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arXiv · 2401.06239

Polynomial slow-fast systems on the Poincar\'e-Lyapunov sphere

Otavio Henrique Perez·Paulo Ricardo da Silva
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Abstract

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.

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Otavio Henrique Perez, Paulo Ricardo da Silva. 2024-01-11. Polynomial slow-fast systems on the Poincar\'e-Lyapunov sphere. https://arxiv.org/abs/2401.06239

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