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

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

2002-03-29

arxiv.org/abs/nlin/0203063v1

Discrete and Continuous Dynamical Systems - Series B 2, 457 (2002)

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

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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