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The generalized recurrent set and strong chain recurrence

  • JIM WISEMAN (a1)

Abstract

Fathi and Pageault have recently shown a connection between Auslander’s generalized recurrent set $\text{GR}(f)$ and Easton’s strong chain recurrent set. We study $\text{GR}(f)$ by examining that connection in more detail, as well as connections with other notions of recurrence. We give equivalent definitions that do not refer to a metric. In particular, we show that $\text{GR}(f^{k})=\text{GR}(f)$ for any $k>0$ , and give a characterization of maps for which the generalized recurrent set is different from the ordinary chain recurrent set.

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The generalized recurrent set and strong chain recurrence

  • JIM WISEMAN (a1)

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