Universal bounds on the entropy of toroidal attractors

2024/03/27 by Macías, P. Montealegre, Sánchez-Gabites, J. J.
#37B35 #37E99 #55N99 #57K99 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2403.18780

Abstract

A toroidal set is a compactum K ⊆ ℝ³ 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).

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