Topological Conjugacy Between Induced Non-autonomous Set-Valued Systems and Subshifts of Finite Type
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Article number | 34 |
Journal / Publication | Qualitative Theory of Dynamical Systems |
Volume | 19 |
Issue number | 1 |
Online published | 1 Feb 2020 |
Publication status | Published - Apr 2020 |
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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.
Research Area(s)
- Chaos, Induced set-valued system, Non-autonomous discrete system, Subshift of finite type, Topological conjugacy, Topological entropy
Citation Format(s)
Topological Conjugacy Between Induced Non-autonomous Set-Valued Systems and Subshifts of Finite Type. / Shao, Hua; Chen, Guanrong; Shi, Yuming.
In: Qualitative Theory of Dynamical Systems, Vol. 19, No. 1, 34, 04.2020.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review