Hyperbolicity, Shadowing, and Bounded Orbits

• K. Lee ^[1] ; C. A. Morales ^[2]
  1. [1] Chungnam National University

     Chungnam National University

     Corea del Sur

     
  2. [2] Universidade Federal do Rio de Janeiro

     Universidade Federal do Rio de Janeiro

     Brasil

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • We show that a linear homeomorphism with the shadowing property of a Banach space is hyperbolic if and only if the set of points with bounded orbit is closed. The proof is based on an auxiliary type of shadowing called bounded shadowing property. We give examples where our result can be applied.