Transitive sensitive subsystems for interval maps

Volume 169 / 2005

Sylvie Ruette Studia Mathematica 169 (2005), 81-104 MSC: Primary 37E05. DOI: 10.4064/sm169-1-6


We prove that for continuous interval maps the existence of a non-empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topological entropy and implies chaos in the sense of Li–Yorke, and we exhibit examples showing that these three notions are distinct.


  • Sylvie RuetteLaboratoire de Mathématiques
    Topologie et Dynamique, Bâtiment 425
    Université Paris-Sud
    F-91405 Orsay Cedex, France

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