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The Conley index over a base


Authors: Marian Mrozek, James F. Reineck and Roman Srzednicki
Journal: Trans. Amer. Math. Soc. 352 (2000), 4171-4194
MSC (2000): Primary 37B30; Secondary 55R70, 37B35, 54H20
DOI: https://doi.org/10.1090/S0002-9947-00-02163-2
Published electronically: May 22, 2000
MathSciNet review: 1466953
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Abstract:

We construct a generalization of the Conley index for flows. The new index preserves information which in the classical case is lost in the process of collapsing the exit set to a point. The new index has most of the properties of the classical index. As examples, we study a flow with a knotted orbit in ${R}^3$, and the problem of continuing two periodic orbits which are not homotopic as loops.


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Additional Information

Marian Mrozek
Affiliation: Instytut Informatyki, Uniwersytet Jagielloński, 30-072 Kraków, Poland
Email: mrozek@ii.uj.edu.pl

James F. Reineck
Affiliation: Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14214-3093
Email: reineck@newton.math.buffalo.edu

Roman Srzednicki
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, 30-059 Kraków, Poland
Email: srzednic@im.uj.edu.pl

DOI: https://doi.org/10.1090/S0002-9947-00-02163-2
Keywords: Isolated invariant set, Conley index, continuation, fiberwise pointed space
Received by editor(s): May 3, 1996
Received by editor(s) in revised form: March 10, 1997
Published electronically: May 22, 2000
Additional Notes: The first author was supported by KBN, Grant 0449/P3/94/06
The third author was supported by KBN, Grant 2 P03A 040 10
Article copyright: © Copyright 2000 American Mathematical Society