Shape and Morse theory of attractors

Lev Kapitanski, Igor Rodnianski

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


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
Issue number2
StatePublished - Feb 2000

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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