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| Format: | Preprint |
| Publié: |
2021
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| Accès en ligne: | https://arxiv.org/abs/2108.12696 |
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| _version_ | 1866909186607022080 |
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| author | Boronski, J. P. |
| author_facet | Boronski, J. P. |
| contents | Let $h : \mathbb{R}^2 \to \mathbb{R}^2$ be an orientation preserving homeomorphism of the plane. For any bounded orbit $\mathcal{O}(x)=\{h^n(x):n\in\mathbb{Z}\}$ there exists a fixed point $x'\in\mathbb{R}^2$ of $h$ linked to $\mathcal{O}(x)$ in the sense of Gambaudo: one cannot find a Jordan curve $C\subseteq\mathbb{R}^2$ around $\mathcal{O}(x)$, separating it from $x'$, that is isotopic to $h(C)$ in $\mathbb{R}^2\setminus\left(\mathcal{O}(x)\cup\{x'\}\right)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_12696 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Linked orbits of homeomorphisms of the plane and Gambaudo-Kolev Theorem Boronski, J. P. Dynamical Systems Algebraic Topology Let $h : \mathbb{R}^2 \to \mathbb{R}^2$ be an orientation preserving homeomorphism of the plane. For any bounded orbit $\mathcal{O}(x)=\{h^n(x):n\in\mathbb{Z}\}$ there exists a fixed point $x'\in\mathbb{R}^2$ of $h$ linked to $\mathcal{O}(x)$ in the sense of Gambaudo: one cannot find a Jordan curve $C\subseteq\mathbb{R}^2$ around $\mathcal{O}(x)$, separating it from $x'$, that is isotopic to $h(C)$ in $\mathbb{R}^2\setminus\left(\mathcal{O}(x)\cup\{x'\}\right)$. |
| title | Linked orbits of homeomorphisms of the plane and Gambaudo-Kolev Theorem |
| topic | Dynamical Systems Algebraic Topology |
| url | https://arxiv.org/abs/2108.12696 |