Repozytorium publikacji - Politechnika Gdańska

In this thesis we continue with developing the E-cohomological Conley index which was introduced by A.Abbondandolo. In particular, we generalize the index to non-gradient flows, we show that it an possesses additional multiplicative structure and we prove the continuation principle. Then, using continuation principle, we show how the computation of the E-cohomological Conley index can be reduced to the computation of the classical Conley index for a gradient flow on a finite-dimensional space. We conclude that the index is isomorphic to the local Morse cohomology on a Hilbert space. Finally, we apply above results to give a short proof of the Arnold conjecture on 2n-dimensional torus in both degenerate and non-degenerate case.

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