The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets

Risong Li and Tianxiu Lu

Complexity, 2020, vol. 2020, 1-12

Abstract:

In this paper, we study some chaotic properties of - dimensional dynamical system of the form where for any is an integer, and is a compact subinterval of the real line for any . Particularly, a necessary and sufficient condition for a cyclic permutation map to be LY-chaotic or h-chaotic or RT-chaotic or D-chaotic is obtained. Moreover, the LY-chaoticity, h-chaoticity, RT-chaoticity, and D-chaoticity of such a cyclic permutation map is explored. Also, we proved that the topological entropy of such a cyclic permutation map is the same as the topological entropy of each of the following maps: if and , and that is sensitive if and only if at least one of the coordinates maps of is sensitive.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:9379628

DOI: 10.1155/2020/9379628

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