Universal bounds on the entropy of toroidal attractors
| Autor: | Macías, P. Montealegre, Sánchez-Gabites, J. J. |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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). |
| Databáze: | arXiv |
| Externí odkaz: |
|