Supremum subsequence entropy for IP-sets
Fundamenta Mathematicae
MSC: Primary 37B40; Secondary 37B05
DOI: 10.4064/fm240714-6-12
Published online: 25 February 2025
Abstract
Let $(X,T)$ be a topological dynamical system and let $A$ be an increasing sequence in $\mathbb N$. We define $h^{*}_A(T)=\sup _{E\subset A}h^E(T)$, where $h^E(T)$ is the topological sequence entropy of $(X,T)$ along the increasing subsequence $E$ of $A$. When $A=\mathbb N$, it was shown in by Huang and Ye (2009) that $h^{*}_A(T)$ takes values in $\{0,\log 2,\log 3,\ldots \}\cup \{\infty \} $. We give some conditions on $A$ under which this assertion still holds. In particular, we show that it is so if $A$ is any IP-set.
