Shift equivalence and the Conley index

John Franks*, David Richeson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


In this paper we introduce filtration pairs for an isolated invariant set of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an invariant of the isolated invariant set. Moreover, the maps defining the shift equivalence can be chosen canonically. Last, we define partially ordered Morse decompositions and prove the existence of Morse set filtrations for such decompositions.

Original languageEnglish (US)
Pages (from-to)3305-3322
Number of pages18
JournalTransactions of the American Mathematical Society
Issue number7
StatePublished - 2000

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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