Scaling law for the critical function of an approximate renormalization

Details Scaling law for the critical function of an approximate renormalization Scaling law for the critical function of an approximate renormalization

2000-05-10

arxiv.org/abs/nlin/0005020v1

Nonlinear Sciences

Chaotic Dynamics

latex article.tex, 5 files, 14 pages, submitted to Nonlinearity

Scientific paper

10.1088/0951-7715/14/4/308

We construct an approximate renormalization for Hamiltonian systems with two degrees of freedom in order to study the break-up of invariant tori with arbitrary frequency. We derive the equation of the critical surface of the renormalization map, and we compute the scaling behavior of the critical function of one-parameter families of Hamiltonians, near rational frequencies. For the forced pendulum model, we find the same scaling law found for the standard map in [Carletti and Laskar, preprint (2000)]. We discuss a conjecture on the link between the critical function of various types of forced pendulum models, with the Bruno function.

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