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