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Une théorie de Morse pour les systèmes hamiltoniens convexes. (French) Zbl 0537.58018

Author’s abstract: ”This paper deals with convex Hamiltonian systems. It is shown that, on any prescribed energy level, either the closed trajectories are infinitely many, or they fulfil a resonance condition. It follows that, generically, there are infinitely many closed trajectories on a prescribed energy level. A dual form of the least action principle, Morse theory, an iteration formula for the index, and Thom’s transversality theorems, are used to obtain these results.”
Reviewer: N.Papaghiuc

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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