The connection matrix in Morse-Smale flows

Author:
James F. Reineck

Journal:
Trans. Amer. Math. Soc. **322** (1990), 523-545

MSC:
Primary 58F12; Secondary 34C40, 58F09

DOI:
https://doi.org/10.1090/S0002-9947-1990-0972705-3

MathSciNet review:
972705

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Abstract: In a Morse-Smale flow with no periodic orbits, it is shown that the connection matrix is unique. In the case of periodic orbits, nonuniqueness can occur. We show that on -manifolds, with some technical assumptions, given a connection matrix for the flow, one can replace the periodic orbits with doubly-connected rest points and obtain a new flow with no periodic orbits having the given connection matrix.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-0972705-3

Keywords:
Conley index,
connection matrix,
continuation,
Morse-Smale flow

Article copyright:
© Copyright 1990
American Mathematical Society