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On the fine structure of the global attractor of a uniformly persistent flow

Rodríguez Sanjurjo, José Manuel (2012) On the fine structure of the global attractor of a uniformly persistent flow. Journal of Differential Equations, 252 (9). pp. 4886-4897. ISSN 0022-0396

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Abstract

We study the internal structure of the global attractor of a uniformly persistent flow. We show that the restriction of the flow to the global attractor has duality properties which can be expressed in terms of certain attractor-repeller decompositions. We also study some natural Morse decompositions of the flow and calculate their Morse equations. These equations provide necessary and sufficient conditions for the existence of attractors with the shape of S-1 or such that their suspension has spherical shape.


Item Type:Article
Uncontrolled Keywords:Uniform persistence; Attractor; Repeller; Robustness; Continuation; Morse equations; Shape
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16728
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