Some properties for the attractors
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For the continuous flows defined on a topological space, we have discussed some properties for the invariant sets and their domains of influence. We have proved the following open problem posed by C. Conley: an attractor in a locally connected compact Hausdorff invariant set has finitely many components. In the meantime, two necessary and sufficient conditions for a set to be an attractor have been given.
KeywordsCompact Hausdorff space Flow Attractor Connected component
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- 11.Eisenberg, M., Topology, New York: Holt, Rinehart and Winston, Inc., 1974.Google Scholar
- 13.Huang Tusen, The note on limit set of a set and the non-wandering set, J. Ningbo University, 1997, 10(2): 1–8.Google Scholar
- 14.Huang Tusen, Compact and asymptotic stability of the set of bounded solutions, J. Hainan Teachers College, 1997, 8: 9–15.Google Scholar