Geodesic
The Conley index in Hilbert spaces and its applications
Studia Mathematica, Tome 134 (1999) no. 3, pp. 217-233 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having asymptotically linear gradient. 
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K Gęba; M. Izydorek; A. Pruszko. The Conley index in Hilbert spaces and its applications. Studia Mathematica, Tome 134 (1999) no. 3, pp. 217-233. doi: 10.4064/sm-134-3-217-233

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