Approximate renormalization with codimension-one fixed point for the break-up of some three-frequency tori

An approximate renormalization transformation is constructed for Hamiltonian systems with three degrees of freedom to study the break-up of invariant tori with a three-dimensional frequency vector from the cubic field Q(tau), where tau (3) + tau (2) - 2 tau - 1 = 0. This renormalization has two fixed points: an attracting one and a hyperbolic one with codimension-one stable manifold. The associated critical exponents that characterize the universality class for the break-up of these invariant tori are computed. (C) 2000 Elsevier Science B.V. All rights reserved.