Vector Fields with the Asymptotic Orbital Pseudo-orbit Tracing Property

• Lee, Manseob ^[1] ; Park Junmi ^[2]
  1. [1] Mokwon University

     Mokwon University

     Corea del Sur

     
  2. [2] Chungnam National University

     Chungnam National University

     Corea del Sur

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 2, 2020
• Idioma: inglés
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• Resumen

  • In this paper, we introduce the notion of the asymptotic orbital pseudo-orbit tracing property for a vector field X of a compact smooth manifold M. We show that if a vector field X has the C1 robust asymptotic orbital pseudo-orbit tracing property, then it is Anosov, and if a C1 generic vector field X has the asymptotic orbital pseudo-orbit tracing property, then it is Anosov. Moreover, we also show our results for divergence-free vector fields and Hamiltonian systems.