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On the topology of the boundary of a basin of attraction

Sánchez Gabites, Jaime Jorge and Rodríguez Sanjurjo, José Manuel (2007) On the topology of the boundary of a basin of attraction. Proceedings of the American Mathematical Society, 135 (12). pp. 4087-4098. ISSN 0002-9939

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Abstract

Suppose phi : M x R -> M is a continuous flow on a locally compact metrizable space M and K is an ( asymptotically stable) attractor. Let D =partial derivative A( K) be the boundary of the basin of attraction of K. In the present paper it will be shown how the Conley index of D plays an important role in determining the topological nature of D and allows one to obtain information about the global dynamics of phi in M.


Item Type:Article
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16805
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