The connection matrix in Morse-Smale flows. II

Author:
James F. Reineck

Journal:
Trans. Amer. Math. Soc. **347** (1995), 2097-2110

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

DOI:
https://doi.org/10.1090/S0002-9947-1995-1290731-9

MathSciNet review:
1290731

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a connection matrix for a Morse-Smale flow on a compact manifold, if there are no periodic orbits of equal or adjacent indices related in the partial order, we show that the periodic orbits can be replaced by doubly connected rest points in such a way that the given connection matrix induces the unique connection matrix for the resulting flow. It follows that for this class of flows, all nonuniqueness in the connection matrix is a consequence of the continuation theorem for connection matrices.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1290731-9

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

Article copyright:
© Copyright 1995
American Mathematical Society