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Science in China Series A: Mathematics

, Volume 44, Issue 7, pp 823–828 | Cite as

Some properties for the attractors

  • Zuohuan Zheng
Article

Abstract

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.

Keywords

Compact Hausdorff space Flow Attractor Connected component 

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Copyright information

© Science in China Press 2001

Authors and Affiliations

  1. 1.Institute of Applied MathematicsAcademy of Mathematics and System Sciences, Chinese Academy of SciencesBeijingChina

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