Renormalization and periodic orbits for Hamiltonian flows

We consider a renormalization group transformation R for analytic Hamiltonians in two or more dimensions, and use this transformation to construct invariant tori, as well as sequences of periodic orbits with rotation vectors approaching that of the invariant torus. The construction of periodic and quasiperiodic orbits is limited to near-integrable Hamiltonians. But as a first step toward a non-perturbative analysis, we extend the domain of R to include any Hamiltonian for which a certain non-resonance condition holds.