Topological Conjugacy Between Induced Non-autonomous Set-Valued Systems and Subshifts of Finite Type

Hua Shao; Guanrong Chen; Yuming Shi

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Topological Conjugacy Between Induced Non-autonomous Set-Valued Systems and Subshifts of Finite Type

Shao Hua ^[1] ; Chen, Guanrong ^[2] ; Shi, Yuming ^[3]
1. [1] Nanjing University of Aeronautics and Astronautics
  
  Nanjing University of Aeronautics and Astronautics
  
  China
2. [2] City University of Hong Kong
  
  City University of Hong Kong
  
  RAE de Hong Kong (China)
3. [3] Shandong University
  
  Shandong University
  
  China
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
Idioma: inglés
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Resumen
- 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.