Local Topological Stability for Diffeomorphisms

• Manseob Lee ^[1]
  1. [1] Mokwon University

     Mokwon University

     Corea del Sur

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
• Idioma: inglés
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• Resumen

  • Let f : M → M be a diffeomorphism of compact smooth Riemannian manifold M, an let ⊂ M be a closed f -invariant set. We obtain conditions for to be topologically stable which is called -topologically stable. Moreover, we prove that if f is C1 robustly -topologically stable then satisfies star condition for f . Then in the above, if a closed f -invariant set is chain transitive (or transitive) then it is hyperbolic for f .