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Renormalization for cubic frequency invariant tori in Hamiltonian systems with two degrees of freedom

C. Chandre
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Abstract

We consider the break-up of invariant tori in Hamiltonian systems with two degrees of freedom with a frequency which belongs to a cubic field. We define and construct renormalization-group transformations in order to determine the threshold of the break-up of these tori. A first transformation is defined from the continued fraction expansion of the frequency, and a second one is defined with a fixed frequency vector in a space of Hamiltonians with three degrees of freedom.

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C. Chandre. 2002-03-29. Renormalization for cubic frequency invariant tori in Hamiltonian systems with two degrees of freedom. https://arxiv.org/abs/nlin/0203063

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