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Inégalités “a priori” pour des tores lagrangiens invariants par des difféomorphismes symplectiques. (‘A priori’ inequalities for Langrangian tori invariant under symplectic diffeomorphisms). (French) Zbl 0717.58020
The author’s result is the generalization of the first Birkhoff theorem on Lipschitz inequalities and the second Birkhoff theorem to the case, when invariant curves are graphs. The method of proving this result is very difficult and interesting. A part of this result was announced in Sémin. Equations Dériv. Partielles 1987/88, Exp. No.14, 24 p. (1988; Zbl 0664.58005)].
Reviewer: D.Nguyen Huu

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37C80 Symmetries, equivariant dynamical systems (MSC2010)
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