Polynomial slow-fast systems on the Poincaré-Lyapunov sphere
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929207527866368 |
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| author | Perez, Otavio Henrique da Silva, Paulo Ricardo |
| author_facet | Perez, Otavio Henrique da Silva, Paulo Ricardo |
| 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_06239 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial slow-fast systems on the Poincaré-Lyapunov sphere Perez, Otavio Henrique da Silva, Paulo Ricardo Dynamical Systems 34C45, 34D15 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. |
| title | Polynomial slow-fast systems on the Poincaré-Lyapunov sphere |
| topic | Dynamical Systems 34C45, 34D15 |
| url | https://arxiv.org/abs/2401.06239 |