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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 μ 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:
37K55Perturbations, KAM for infinite-dimensional systems
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37C55Periodic and quasiperiodic flows and diffeomorphisms
70H08Nearly integrable Hamiltonian systems, KAM theory
70H09Perturbation theories (mechanics of particles and systems)
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