Shape and Morse theory of attractors

Lev Kapitanski, Igor Rodnianski

Research output: Contribution to journalArticle

42 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)218-242
Number of pages25
JournalCommunications on Pure and Applied Mathematics
Volume53
Issue number2
StatePublished - Feb 2000
Externally publishedYes

Fingerprint

Morse Theory
Attractor
Continuous System
Global Attractor
Metric space
State Space
Inclusion
Equivalence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Shape and Morse theory of attractors. / Kapitanski, Lev; Rodnianski, Igor.

In: Communications on Pure and Applied Mathematics, Vol. 53, No. 2, 02.2000, p. 218-242.

Research output: Contribution to journalArticle

Kapitanski, Lev ; Rodnianski, Igor. / Shape and Morse theory of attractors. In: Communications on Pure and Applied Mathematics. 2000 ; Vol. 53, No. 2. pp. 218-242.
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