Shape properties of the boundary of attractors



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Sánchez Gabites, Jaime Jorge and Rodríguez Sanjurjo, José Manuel (2007) Shape properties of the boundary of attractors. Glasnik Matematicki Series III, 42 (1). pp. 117-130. ISSN 0017-095X

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A compact stable attractor K of a continuous flow on a locally compact metric space is shape equivalent to a compact positively invariant neighbourhood P in its basin of attraction, the shape equivalence being induced by the inclusion map. In the present article a simple counterexample is given to show that ∂K is in general not shape equivalent to ∂P , and an inquiry is set afoot as to the circumstances under which ∂K is shape equivalent to or shape dominates ∂P .

Item Type:Article
Uncontrolled Keywords:Dynamical systems, attractors, boundary of attractors, shape
Subjects:Sciences > Mathematics > Topology
ID Code:21809
Deposited On:12 Jun 2013 13:01
Last Modified:19 Feb 2019 13:05

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