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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 for infinite-dimensional systems 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies 37C55 Periodic and quasiperiodic flows and diffeomorphisms 70H08 Nearly integrable Hamiltonian systems, KAM theory 70H09 Perturbation theories (mechanics of particles and systems)
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