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

C. Chandre·R. S. MacKay
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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 $Q(τ)$, where $τ^3+τ^2-2τ-1=0$. 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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C. Chandre, R. S. MacKay. 2000-01-17. Approximate renormalization for the break-up of invariant tori with three frequencies. https://doi.org/10.1016/s0375-9601(00)00599-5

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