Geodesic
An approximation scheme for defining the Conley index of isolated critical points
Differencialʹnye uravneniâ, Tome 40 (2004) no. 11, pp. 1462-1467.

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In the present paper, we study isolated critical points of functionals dened 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. 
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     author = {N. A. Bobylev and A. V. Bulatov and Yu. O. Kuznetsov},
     title = {An approximation scheme for defining the {Conley} index of isolated critical points},
     journal = {Differencialʹnye uravneni\^a},
     pages = {1462--1467},
     publisher = {mathdoc},
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     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DE_2004_40_11_a2/}
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N. A. Bobylev; A. V. Bulatov; Yu. O. Kuznetsov. An approximation scheme for defining the Conley index of isolated critical points. Differencialʹnye uravneniâ, Tome 40 (2004) no. 11, pp. 1462-1467. http://geodesic.mathdoc.fr/item/DE_2004_40_11_a2/