The Chain Properties and Average Shadowing Property of Iterated Function Systems

• Wu, Xinxing ^[1] ; Wang, Lidong ^[3] ; Liang, Jianhua ^[2]
  1. [1] Southwest Petroleum University

     Southwest Petroleum University

     China

     
  2. [2] Jilin University

     Jilin University

     China

     
  3. [3] Zhuhai College of Jilin University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 1, 2018, págs. 219-227
• Idioma: inglés
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  • This note proves that an iterated function system is chain transitive (resp., chain mixing, transitive) if and only if the step skew product corresponding to the iterated function system is chain transitive (resp., chain mixing, transitive). As an application, it is obtained that an iterated function system with the (asymptotic) average shadowing property is chain mixing, improving the main results in Bahabadi (Georgian Math J 22:179–184, 2015).