Geodesic
On strong chain recurrence for maps
Katsuya Yokoi1
1 Department of Mathematics Jikei University School of Medicine Chofu, Tokyo 182-8570, Japan
Annales Polonici Mathematici, Tome 114 (2015) no. 2, pp. 165-177 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap114-2-6
Keywords: paper concerned strong chain recurrence introduced easton investigate depth transfinite sequence nested closed invariant sets obtained iterating process taking strong chain recurrent points which related form central sequence due birkhoff note existence lyapunov function which decreasing off strong chain recurrent set application necessary sufficient condition coincidence strong chain recurrence set chain recurrence set several examples given illustrate difference between concepts strong chain recurrence chain recurrence

Katsuya Yokoi 1

1 Department of Mathematics Jikei University School of Medicine Chofu, Tokyo 182-8570, Japan 
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Katsuya Yokoi. On strong chain recurrence for maps. Annales Polonici Mathematici, Tome 114 (2015) no. 2, pp. 165-177. doi: 10.4064/ap114-2-6

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