Shape and Morse theory of attractors

Lev Kapitanski; Igor Rodnianski

doi:10.1002/(SICI)1097-0312(200002)53:2<218::AID-CPA2>3.0.CO;2-W

Shape and Morse theory of attractors

Lev Kapitanski, Igor Rodnianski

Mathematics

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

Abstract

We study the shape (in the sense of Borsuk) of attractors of continuous semidynamical systems on general metric spaces. We show, in particular, that the natural inclusion of the global attractor into the state space is a shape equivalence. This and other results of the paper are used to develop an elementary Morse theory of an attractor.

Original language	English (US)
Pages (from-to)	218-242
Number of pages	25
Journal	Communications on Pure and Applied Mathematics
Volume	53
Issue number	2
DOIs	https://doi.org/10.1002/(SICI)1097-0312(200002)53:2<218::AID-CPA2>3.0.CO;2-W
State	Published - Feb 2000

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1002/(SICI)1097-0312(200002)53:2<218::AID-CPA2>3.0.CO;2-W

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AB - We study the shape (in the sense of Borsuk) of attractors of continuous semidynamical systems on general metric spaces. We show, in particular, that the natural inclusion of the global attractor into the state space is a shape equivalence. This and other results of the paper are used to develop an elementary Morse theory of an attractor.

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Shape and Morse theory of attractors

Abstract

All Science Journal Classification (ASJC) codes

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