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The Conley index over a base
Author(s):
Marian
Mrozek;
James
F.
Reineck;
Roman
Srzednicki
Journal:
Trans. Amer. Math. Soc.
352
(2000),
4171-4194.
MSC (2000):
Primary 37B30;
Secondary 55R70, 37B35, 54H20
Posted:
May 22, 2000
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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  , 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 Jagiellonski, 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 Jagiellonski, 30-059 Kraków, Poland
Email:
srzednic@im.uj.edu.pl
DOI:
10.1090/S0002-9947-00-02163-2
PII:
S 0002-9947(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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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