KAM proofs of existence of invariant surfaces for isoenergetically degenarate (non-twist) Hamiltonian flows are known to present significant difficulties. We will demonstrate how the renormalization group transformation, a non-perturbative technique, can be used to

study problems which are traditionally the subject of the KAM theory. We will also mention some recent results about universality and self-similarity of critical Hamiltonian flows whose invariant tori are at the break-up.