Topological Entropy of Iterated Set-Valued Dynamical Systems

• Autores: Xiaofang Luo
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01017-9
• Enlaces
  • Texto completo
• Resumen

  • This paper studies topological entropy and pseudo-entropy of iterated set-valued function systems. Firstly, the notions of topological entropy defined by separating and spanning sets and by open covers are introduced respectively, and they are proved equivalent, then a formula is obtained for the topological entropy of an iterated set-valued function system concerning the corresponding skew product system, and topological entropy of iterated set-valued function systems is a topological conjugacy invariant. Finally, the notions of pseudo-entropy of set-valued function systems and iterated set-valued function systems are introduced and it is proved that the pseudoentropy is equal to the topological entropy of iterated set-valued function systems.

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