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Algebraic transition matrices in the Conley index theory
Author(s):
Robert
Franzosa;
Konstantin
Mischaikow
Journal:
Trans. Amer. Math. Soc.
350
(1998),
889-912.
MSC (1991):
Primary 58F35;
Secondary 58F30, 35K57
MathSciNet review:
1360223
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Abstract:
We introduce the concept of an algebraic transition matrix. These are degree zero isomorphisms which are upper triangular with respect to a partial order. It is shown that all connection matrices of a Morse decomposition for which the partial order is a series-parallel admissible order are related via a conjugation with one of these transition matrices. This result is then restated in the form of an existence theorem for global bifurcations. Simple examples of how these results can be applied are also presented.
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Additional Information:
Robert
Franzosa
Affiliation:
Department of Mathematics, University of Maine, Orono, Maine 04469
Email:
franzosa@gauss.umemat.maine.edu
Konstantin
Mischaikow
Affiliation:
Center for Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email:
mischail@math.gatech.edu
DOI:
10.1090/S0002-9947-98-01666-3
PII:
S 0002-9947(98)01666-3
Keywords:
Conley index,
connection matrix,
transition matrix,
bistable attractor,
travelling waves
Received by editor(s):
January 3, 1995
Received by editor(s) in revised form:
October 4, 1995
Additional Notes:
Research was supported in part by NSF Grant DMS-9101412. Part of this paper was written while the second author was visiting the Instituto de Ciencias Mathematicas de São Carlo of the Universidade de São Paulo. He would like to take this opportunity to thank the members of the institute for their warm hospitality.
Copyright of article:
Copyright
1998,
American Mathematical Society
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