Lower-dimensional tori in multi-scale, nearly integrable Hamiltonian systems (Q512457)

Topological properties of multi-scale real analytic, nearly integrable Hamiltonian systems when the integrable part of the degenerate Hamiltonian function depends on a part of action variables only are investigated. An important problem in studying multi-scale Hamiltonian systems is to identify suitable conditions for existence of quasi-periodic motions, or equivalently, the persistence, after taking into account the perturbation part of the Hamiltonian function, of the quasi-periodic invariant tori. A review of results published in the last two decades is given.