Universal bounds on the entropy of toroidal attractors
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913286892552192 |
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| author | Macías, P. Montealegre Sánchez-Gabites, J. J. |
| author_facet | Macías, P. Montealegre Sánchez-Gabites, J. J. |
| contents | A toroidal set is a compactum $K \subseteq \mathbb{R}^3$ which has a neighbourhood basis of solid tori. We study the topological entropy of toroidal attractors $K$, bounding it from below in terms of purely topological properties of $K$. In particular, we show that for a toroidal set $K$, either any smooth attracting dynamics on $K$ has an entropy at least $\log 2$, or (up to continuation) $K$ admits smooth attracting dynamics which are stationary (hence with a zero entropy). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal bounds on the entropy of toroidal attractors Macías, P. Montealegre Sánchez-Gabites, J. J. Dynamical Systems Geometric Topology 57K99, 37B35, 37E99, 55N99 A toroidal set is a compactum $K \subseteq \mathbb{R}^3$ which has a neighbourhood basis of solid tori. We study the topological entropy of toroidal attractors $K$, bounding it from below in terms of purely topological properties of $K$. In particular, we show that for a toroidal set $K$, either any smooth attracting dynamics on $K$ has an entropy at least $\log 2$, or (up to continuation) $K$ admits smooth attracting dynamics which are stationary (hence with a zero entropy). |
| title | Universal bounds on the entropy of toroidal attractors |
| topic | Dynamical Systems Geometric Topology 57K99, 37B35, 37E99, 55N99 |
| url | https://arxiv.org/abs/2403.18780 |