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Existence et non existence de tores invariants par des difféomorphismes symplectiques. (Existence and nonexistence of invariant tori of symplectic diffeomorphisms). (French) Zbl 0664.58005
Sémin., Équations Dériv. Partielles 1987/1988, Exp. No. 14, 24 p. (1988).
The paper is devoted to a generalization of a theory of G. D. Birkhoff [Acta Math. 43, 1-119 (1920)], to the study of invariant Lagrangian tori of symplectic diffeomorphisms of \(T^*T^ n\). Accordingly, one discusses a monotonicity property of such diffeomorphisms and their perturbations, one proves Lipschitz inequalities for invariant Lagrangian tori which are graphs, existence and nonexistence of invariant tori under various hypotheses etc. The results will be exposed completely in a forthcoming paper by the author.
Reviewer: I.Vaisman

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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