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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the two definitions of the Conley index

Author: Henry L. Kurland
Journal: Proc. Amer. Math. Soc. 106 (1989), 1117-1130
MSC: Primary 58F25
MathSciNet review: 982405
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Abstract: The two definitions of the homotopy equivalences between Conley index spaces of an isolated invariant set, the original one of Conley [C] as completed by the author in [K1] and the more recent definition of Salamon [S], are shown to define the same homotopy classes without reference to the difficult proof of [K1] showing the Conley index to be a connected simple system. The equivalences of the original definition are useful in describing certain geometric situations in terms of the index; examples are given.

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Keywords: Isolated invariant set, Conley index, connected simple system, homology of the Conley index, boundary layer, common squeeze time, flow map
Article copyright: © Copyright 1989 American Mathematical Society