Noncompact chain recurrence and attraction.

*(English)*Zbl 0759.58031The author intends to extend a theorem of C. Conley from the setting of dynamical systems on compact metric spaces to metric spaces that are only locally compact, although the basic results are analogous to Conley’s theorem that characterizes the chain recurrent set of \(f\) in terms of the attractors of \(f\) and their basins of attraction. According to the results by the author the given metric is of primary importance rather than the topology it generated. The author gives the results in this note that depend on the topology induced by a metric rather than on the particular choice of the metric.

Reviewer: Y.Kozai (Tokyo)

##### MSC:

37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |

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\textit{M. Hurley}, Proc. Am. Math. Soc. 115, No. 4, 1139--1155 (1992; Zbl 0759.58031)

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##### References:

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