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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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Abstract:

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: http://dx.doi.org/10.1090/S0002-9947-00-02488-0
PII: S 0002-9947(00)02488-0
Received by editor(s): June 22, 1998
Published electronically: March 24, 2000
Article copyright: © Copyright 2000 American Mathematical Society