On Integrable Models Close To Slow-Fast Hamiltonian Systems

Abstract

Abstract: We construct a family of completely integrable systems εN-close to a slow-fast Hamiltonian system with two degrees of freedom which is described in the framework of the averaging method over slow-fast phase spaces with S1-symmetry. Our approach is based on the free-coordinate normalization procedure for slow-fast Hamiltonian system with two degree of freedom.