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

Ekeland, Ivar

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1, 19-78 (1984).

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

Keywords:

Morse index; closed trajectories; periodic solutions; transversality

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