  We study the stability and breakup of invariant tori in Hamiltonian flows
using a combination of Kolmogorov-Arnold-Moser (KAM) theory and
renormalization-group techniques. We implement the scheme numerically for a
family of Hamiltonians quadratic in the actions to analyze the strong coupling
regime. We show that the KAM iteration converges up to the critical coupling at
which the torus breaks up. Adding a renormalization consisting of a rescaling
of phase space and a shift of resonances allows us to determine the critical
coupling with higher accuracy. We determine a nontrivial fixed point and its
universality properties.
