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Une approche variationnelle des orbites quasi-périodiques des systèmes hamiltoniens. (A variational approach to quasiperiodic orbits of Hamiltonian systems.). (French) Zbl 0698.70015
Summary: After giving new functional analytic proofs of results on (topological) invariant tori and quasi-periodic orbits, we state some elements of the calculus of variations in mean in order to characterize the quasi- periodic orbits of the Hamiltonian systems as critical points of certain functional on Banach spaces. Finally, we prove Percival’s Principle and very shortly we examine the relations with our variational approach.

MSC:
70H30 Other variational principles in mechanics
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
37C55 Periodic and quasi-periodic flows and diffeomorphisms
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