An approximation scheme for defining the conley index of isolated critical points

In the present paper, we study isolated critical points of functionals defined on a real separable Hilbert space H and satisfying the H-properness condition. We introduce the notion of Conley index of an isolated critical point and prove that it is homotopy invariant. The scheme suggested here for d...

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Bibliographic Details
Published in:Differential equations 2004-01, Vol.40 (11), p.1539-1544
Main Authors: Bobylevy, N. A., Bulatov, A. V., Kuznetsov, Yu. O.
Format: Article
Language:English
Subjects:
Approximation
Constrictions
Critical point
Differential equations
Functionals
Hilbert space
Invariants
Mathematical analysis
Studies
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Online Access:Get full text
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Summary:In the present paper, we study isolated critical points of functionals defined on a real separable Hilbert space H and satisfying the H-properness condition. We introduce the notion of Conley index of an isolated critical point and prove that it is homotopy invariant. The scheme suggested here for defining the Conley index is based on the application of finite-dimensional Conley index theory to finite-dimensional restrictions of the functional to be studied.[PUBLICATION ABSTRACT]
ISSN:0012-2661
1608-3083
DOI:10.1007/PL00021822