A Note on Topological Average Shadowing Property Via Uniformity

• Seyyed Alireza Ahmadi ^[1] ; Xinxing Wu ^[2]
  1. [1] University of Sistan and Baluchestan

     University of Sistan and Baluchestan

     Irán

     
  2. [2] Southwest Petroleum University

     Southwest Petroleum University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
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• Resumen

  • We study topological ergodic shadowing, topological d shadowing and topological average shadowing property for a continuous map on a uniform space and show that they are equivalent for a uniformly continuous map with topological shadowing on a compact uniform space. Furthermore, we prove that topological average shadowing property with Lyapunov stability implies topological ergodicity.