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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

    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
  • Idioma: inglés
  • DOI: 10.1007/s12346-020-00369-2
  • Enlaces
  • 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.

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