  We construct an approximate renormalization transformation for Hamiltonian
systems with three degrees of freedom in order to study the break-up of
invariant tori with three incommensurate frequencies which belong to the cubic
field $Q(\tau)$, where $\tau^3+\tau^2-2\tau-1=0$. This renormalization has two
fixed points~: a stable one and a hyperbolic one with a codimension one stable
manifold. We compute the associated critical exponents that characterize the
universality class for the break-up of the invariant tori we consider.
