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
  • Texto completo (pdf)
• 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.