Shadowing Property and Invariant Measures Having Full Supports

• Moriyasu Kazumine ^[3] ; Sakai Kazuhiro ^[1] ; Sumi Naoya ^[2]
  1. [1] Utsunomiya University

     Utsunomiya University

     Japón

     
  2. [2] Kumamoto University

     Kumamoto University

     Chuo-ku, Japón

     
  3. [3] Tokushima University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
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  • We consider the shadowing property from the measure theoretical view point. Let f be a homeomorphism of a compact metric space. Then f has the shadowing property on the chain recurrent set if and only if there exists a shadowable f-invariant measure having full support. Suppose that f does not have the shadowing property. Then, if there exists a f-invariant measure having full support, then, generically, every f-invariant measure is not shadowable.