Hyperbolicity, Shadowing, and Bounded Orbits

K. Lee; C. A. Morales

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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.
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