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Mathematics > Dynamical Systems
Title: Universal bounds on the entropy of toroidal attractors
(Submitted on 27 Mar 2024)
Abstract: 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).
Submission history
From: Jaime Jorge Sánchez-Gabites [view email][v1] Wed, 27 Mar 2024 17:28:37 GMT (70kb,D)
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