Entropy for A-coupled-expanding Maps and Chaos

Abstract

The concept of "$A$-coupled-expanding" map for a transition matrix $A$ has been studied as one of the most important criteria of chaos in the past years. In this paper, the lower bound of the topological entropy for strictly $A$-coupled-expanding maps is studied as a criterion for chaos in the sense of Li-Yorke, which is less conservative and more generalized than the latest result is presented. Furthermore, some conditions for $A$-coupled-expanding maps excluding the strictness to be factors of subshifts of finite type are derived. In addition, the topological entropy of partition-$A$-coupled-expanding map, which is put forward in this paper, is further estimated on compact metric spaces. Particularly, the topological entropy for partition-$A$-coupled-expanding circle maps is given, with that for the Kasner map being calculated for illustration and verification.