  In this article, we describe a new renormalization-group scheme for analyzing
the breakup of invariant tori for Hamiltonian systems with two degrees of
freedom. The transformation, which acts on Hamiltonians that are quadratic in
the action variables, combines a rescaling of phase space and a partial
elimination of irrelevant (non-resonant) frequencies. It is implemented
numerically for the case applying to golden invariant tori. We find a
nontrivial fixed point and compute the corresponding scaling and critical
indices. If one compares flows to maps in the canonical way, our results are
consistent with existing data on the breakup of golden invariant circles for
area-preserving maps.
