Topological conjugacy between induced non-autonomous set-valued systems and subshifts of finite type

Hua Shao; Guanrong Chen; Yuming Shi

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arXiv · 1903.01079

Topological conjugacy between induced non-autonomous set-valued systems and subshifts of finite type

Hua Shao·Guanrong Chen·Yuming Shi

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Abstract

This paper establishes topological (equi-)semiconjugacy and (equi-)conjugacy between induced non-autonomous set-valued systems and subshifts of finite type. First, some necessary and sufficient conditions are given for a non-autonomous discrete system to be topologically semiconjugate or conjugate to a subshift of finite type. Further, several sufficient conditions for it to be topologically equi-semiconjugate or equi-conjugate to a subshift of finite type are obtained. Consequently, estimations of topological entropy and several criteria of Li-Yorke chaos and distributional chaos in a sequence are derived. Second, the relationships of several related dynamical behaviors between the non-autonomous discrete system and its induced set-valued system are investigated. Based on these results, the paper furthermore establishes the topological (equi-)semiconjugacy and (equi-)conjugacy between induced set-valued systems and subshifts of finite type. Consequently, estimations of the topological entropy for the induced set-valued system are obtained, and several criteria of Li-Yorke chaos and distributional chaos in a sequence are established. Some of these results not only extend the existing related results for autonomous discrete systems to non-autonomous discrete systems, but also relax the assumptions of the counterparts in the literature. Two examples are finally provided for illustration.

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BibTeX RIS

Hua Shao, Guanrong Chen, Yuming Shi. 2019-03-04. Topological conjugacy between induced non-autonomous set-valued systems and subshifts of finite type. https://arxiv.org/abs/1903.01079

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