A renormalization group for Hamiltonians, with applications to KAM tori

Abstract

We describe a family of renormalization group transformations which apply to the problem of stability of invariant tori for analytic Hamiltonians. Each of these transformations corresponds to a fixed rotation vector, within a certain class of vectors in ${\mathbb R}^d$. As an application, we prove a KAM-type theorem that yields analytic invariant $d$-tori depending analytically on the Hamiltonian.