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KAM-stable Hamiltonians. (English) Zbl 0951.37038
An original method of studying small perturbations of highly degenerate Hamiltonians is presented. The approach is based on embedding the perturbated Hamiltonian in a family of Hamiltonians depending on an external multidimensional parameter \(\mu\) and thus achieve full control of the frequencies. The invariant tori of the original Hamiltonian system is picked out using the fact that the invariant tori of the whole family constitute a Whitney-smooth foliation.

MSC:
37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37C55 Periodic and quasi-periodic flows and diffeomorphisms
70H08 Nearly integrable Hamiltonian systems, KAM theory
70H09 Perturbation theories for problems in Hamiltonian and Lagrangian mechanics
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