The set of recurrent points of a continuous self-map on an interval and strong chaos

  • Lidong Wang
  • Gongfu Liao
  • ZhenYan Chu
  • XiaoDong Duan
Article

Abstract

In this paper, we discuss a continuous self-map of an interval and the existence of an uncountable strongly chaotic set. It is proved that if a continuous self-map of an interval has positive topological entropy, then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.

AMS Mathematics Subject Classification

28D20 54H20 58F11 58F13 

Key word and phrases

Strong chaos topological entropy recurrence regular shift invariant 

Copyright information

© Korean Society for Computational and Applied Mathematics 2004

Authors and Affiliations

  • Lidong Wang
    • 1
  • Gongfu Liao
    • 2
  • ZhenYan Chu
    • 1
  • XiaoDong Duan
    • 1
  1. 1.The Research Institute of Nonlinear Information & TechnologyDalian Nationalities UniversityDalianP. R. China
  2. 2.The Research Institute of MathematicsJilin UniversityChangchunP. R. China

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