Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
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 $ 2$-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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Keywords: Conley index, connection matrix, continuation, Morse-Smale flow
Article copyright: © Copyright 1990 American Mathematical Society