On the renormalization of Hamiltonian flows, and critical invariant tori (Q1599883)

We analyze a renormalization group transformation \(\mathcal R\) for partially analytic Hamiltonians, with emphasis on what seems to be needed for the construction of non-integrable fixed points. Under certain assumptions, which are supported by numerical data in the golden mean case, we prove that such a fixed point has a critical invariant torus. The proof is constructive and can be used for numerical computations. We also relate \(\mathcal R\) to a renormalization group transformation for commuting maps.