The Conley index and the critical groups via an extension of Gromoll-Meyer theory
Keywords
Gromoll-Meyer pairs, Conley index pairs, dynamically isolated set, isolating invariant neighbourhoods, invariance properties of the Conley indexAbstract
We investigate, in a variational setting, the relationship between the Gromoll-Meyer pairs of {\it a dynamically isolated critical set}\/ and the Conley index pairs of its {\it isolating invariant neighbourhoods}. We show that the information given by the critical groups of such a set is equivalent to that given by the Conley index. This allows us to derive - in a non-compact setting - various invariance properties for the Conley index from those of the critical groups, as well as a formula relating the degree of a gradient vector field in an isolating neighbourhood to the Conley index pair associated with it.Downloads
Published
1996-03-01
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1.
CHANG, Kung Ching and GHOUSSOUB, N. The Conley index and the critical groups via an extension of Gromoll-Meyer theory. Topological Methods in Nonlinear Analysis. Online. 1 March 1996. Vol. 7, no. 1, pp. 77 - 93. [Accessed 20 September 2024].
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