Distributional Chaos on Uniform Spaces

• Shah, Sejal ^[1] ; Das, Tarun ^[2] ; Das Ruchi ^[2]
  1. [1] Maharaja Sayajirao University of Baroda

     Maharaja Sayajirao University of Baroda

     India

     
  2. [2] University of Delhi

     University of Delhi

     India

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
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• Resumen

  • We introduce and study here the notion of distributional chaos on uniform spaces. We prove that if a uniformly continuous self-map of a uniform locally compact Hausdorff space has topological weak specification property then it admits a topologically distributionally scrambled set of type 3. This extends result due to Sklar and Smítal (J Math Anal Appl 241:181–188, 2000). We also justify through examples necessity of the conditions in the hypothesis of the main result.