Shift Equivalence and the Conley Index

In this paper we introduce filtration pairs for isolated invariant sets 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. Lastly, we define partially ordered Morse decompositions and prove the existence of Morse set filtrations for such decompositions.

• Publication year

  1999

• Venue

  Transactions of the American Mathematical Society

• Publication date

  1999-10-29

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1090/S0002-9947-00-02488-0arXiv math/9910171
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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