Approximate renormalization for the break-up of invariant tori with three frequencies

Details Approximate renormalization for the break-up of invariant tori with three frequencies Approximate renormalization for the break-up of invariant tori with three frequencies

2000-01-17

arxiv.org/abs/nlin/0001033v1

Physics Letters A 275 (2000) 394

Nonlinear Sciences

Chaotic Dynamics

5 pages, REVTeX

Scientific paper

10.1016/S0375-9601(00)00599-5

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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