Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems

We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for 3 degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.