Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds

Abstract

We investigate S¹-invariant Hamiltonian systems on compact 4-dimensional symplectic manifolds with free symplectic action of a circle. We show that, in a rather general case, such systems generate ergodic flows of types (quasiperiodic and nilpotent) on their isoenergetic surfaces. We solve the problem of straightening of these flows.