Pointwise Recurrence on Local Dendrites

• Ghassen, Askri ^[2] ; Naghmouchi Issam ^[1]
  1. [1] University of Carthage

     University of Carthage

     Túnez

     
  2. [2] Bizerte Preparatory Engineering Institute
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
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• Resumen

  • In this paper, we prove that if X is a local dendrite different from the circle and f:X→X is a continuous map then f is pointwise recurrent if and only if it is a homeomorphism such that every cut point is periodic. Meanwhile, we show in the case of dendrites that the set of almost periodic points is a continuum and equals to the union of all ω-limit sets provided that the omega limit map is continuous and we show that it is only a necessary condition for the continuity of the omega limit map. We end the paper by suggesting some new open problems.