C. Chandre, R.S. MacKay
Approximate renormalization for the break-up of invariant tori with three frequencies
(27K, REVTeX)
ABSTRACT. 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.