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On strong chain recurrence for maps

Volume 114 / 2015

Katsuya Yokoi Annales Polonici Mathematici 114 (2015), 165-177 MSC: Primary 37B20, 37B25. DOI: 10.4064/ap114-2-6


This paper is concerned with strong chain recurrence introduced by Easton. We investigate the depth of the transfinite sequence of nested, closed invariant sets obtained by iterating the process of taking strong chain recurrent points, which is a related form of the central sequence due to Birkhoff. We also note the existence of a Lyapunov function which is decreasing off the strong chain recurrent set. As an application, we give a necessary and sufficient condition for the coincidence of the strong chain recurrence set and the chain recurrence set. Several examples are given to illustrate the difference between the concepts of strong chain recurrence and chain recurrence.


  • Katsuya YokoiDepartment of Mathematics
    Jikei University School of Medicine
    Chofu, Tokyo 182-8570, Japan

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