Devaney Orbit-State Chaos of Multiple Mappings from a Set-Valued View

• Yingcui Zhao ^[1] ; Lixin Jiao ^[2]
  1. [1] Dongguan University of Technology

     Dongguan University of Technology

     China

     
  2. [2] Guangzhou Polytechnic University
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 4, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Hou and Wang introduced multiple mappings arising from iterated function systems in [1]. Such mappings form a special class of set-valued maps. In this paper, the definitions of periodic point, orbit-state transitivity, sensitivity and Devaney orbit-state chaos of multiple mappings are introduced from a set-valued perspective. Here orbitstate transitivity is a reachability property defined relative to the attainable orbit-state space Ran(F) ⊂ K(X), rather than classical transitivity on X. The relation between multiple mappings and their continuous self-maps is investigated and it is demonstrated that the corresponding properties of multiple mappings and their constituent continuous self-maps do not imply each other in terms of periodic points or orbit-state transitivity. Sufficient conditions for multiple mappings to exhibit periodic points, orbit-state transitivity and sensitivity are provided separately. Meanwhile, it is proved that orbit-state transitivity combined with a dense periodic point set implies sensitivity.

    In addition, a sufficient condition for multiple mappings to be Devaney orbit-state chaotic is presented.

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