00-25 C. Chandre, R.S. MacKay

Approximate renormalization for the break-up of invariant tori with three frequencies (27K, REVTeX) Jan 17, 00

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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.

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