Invariant tori for a class of singly thermostated hamiltonians

Abstract

Let H be a C r proper hamiltonian on T * Σ where Σ = R or T and r > 4. This paper proves sufficient conditions for the existence of a positive measure set of invariant KAM tori in an associated singly thermostated vector field on T * Σ × R. We apply this result to 4 important single thermostats in the literature. This extends results of Legoll, Luskin & Moeckel [7,8].