Shift equivalence and the Conley index

Authors:
John Franks and David Richeson

Journal:
Trans. Amer. Math. Soc. **352** (2000), 3305-3322

MSC (2000):
Primary 37B30

Published electronically:
March 24, 2000

MathSciNet review:
1665329

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**John Franks**

Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730

Email:
john@math.nwu.edu

**David Richeson**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48023-1027

Email:
richeson@math.msu.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02488-0

Received by editor(s):
June 22, 1998

Published electronically:
March 24, 2000

Article copyright:
© Copyright 2000
American Mathematical Society