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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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
MathSciNet review: 1290731
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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: http://dx.doi.org/10.1090/S0002-9947-1995-1290731-9
PII: S 0002-9947(1995)1290731-9
Keywords: Conley index, connection matrix, Morse-Smale flow
Article copyright: © Copyright 1995 American Mathematical Society