Coisotropic quasi-periodic motions near the relative equilibrium of a Hamiltonian system

Abstract

We consider the Hamiltonian system which is invariant under locally Hamiltonian (non-Poissonian) action of torus. We show that when a certain set of conditions is satisfied the majority of motions in a sufficiently small neighbourhood of system’s relative equilibrium are quasi-periodic and cover coisotropic invariant tori.