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Shift equivalence and the Conley index
Author(s):
John
Franks;
David
Richeson
Journal:
Trans. Amer. Math. Soc.
352
(2000),
3305-3322.
MSC (2000):
Primary 37B30
Posted:
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:
10.1090/S0002-9947-00-02488-0
PII:
S 0002-9947(00)02488-0
Received by editor(s):
June 22, 1998
Posted:
March 24, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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