A KAM-Type Theorem for Generalized Hamiltonian Systems (Communications in Mathematical Research, 2021)
In this paper we mainly concern the persistence of lower-dimensionalinvariant tori in generalized Hamiltonian systems. Here the generalized Hamiltoniansystems refer to the systems which may admit a distinct number of action and anglevariables. In particular, system under consideration can be odd dimensional. Underthe Rüssmann type non-degenerate condition, we proved that the majority of thelower-dimension invariant tori of the integrable systems in generalized Hamiltoniansystem are persistent under small perturbation. The surviving lower-dimensional torimight be elliptic, hyperbolic, or of mixed type.