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

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Publication:1429007
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DOI10.1007/BF02936114zbMath1043.37032MaRDI QIDQ1429007

Xiaodong Duan, Gongfu Liao, Lidong Wang, Zhenyan Chu

Publication date: 29 March 2004

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)


zbMATH Keywords

recurrencetopological entropystrong chaosregular shift invariant


Mathematics Subject Classification ID

Entropy and other invariants (28D20) Topological entropy (37B40) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35) Dynamical systems involving maps of the interval (37E05)


Related Items

A chaotic function with a distributively scrambled set of full Lebesgue measure ⋮ Distributional chaos and factors ⋮ Distributional chaos revisited



Cites Work

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  • Dynamics in one dimension
  • Every chaotic interval map has a scrambled set in the recurrent set
  • No Division Implies Chaos
  • Period Three Implies Chaos
  • Measures of Chaos and a Spectral Decomposition of Dynamical Systems on the Interval
  • Set of almost periodic points of a continuous self-map of an interval
  • Some remarks on almost periodic transformations
  • Orbit-closure decompositions and almost periodic properties
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