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Topological Complexity: Entropy Point, Metric Mean Dimension in Control Systems

  • Rui Yang [1] ; Ercai Chen [1] ; Xiaoyao Zhou [1]
    1. [1] Nanjing Normal University

      Nanjing Normal University

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
  • Idioma: inglés
  • Enlaces
  • Resumen
    • We introduce two new notions to describe the topological complexity of control systems. We first introduce a notion called entropy point to characterize zero and positive outer invariance entropy systems, then we introduce a notion called metric mean dimension to characterize the growth of infinite outer invariance entropy systems and establish a variational principle for it in terms of local entropy function that is related to outer invariance entropy. Finally, we establish a product invariance entropy formula under some conditions.

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