Slow entropy for noncompact sets and variational principle
Abstract
This paper defines and discusses the dimension notion of topological slow entropy of any subset for Zd actions. Also, the notion of measure-theoretic slow entropy for Zd actions is presented, which is modified from Brin and Katok [2]. Relations between Bowen topological entropy [3,17] and topological slow entropy are studied in this paper, and several examples of the topological slow entropy in a symbolic system are given. Specifically, a variational principle is proved.
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