Abstract
We construct an approximate renormalization forHamiltonian systems with two degrees of freedom in orderto study the break-up of invariant tori with arbitraryfrequency. We derive the equation of the critical surfaceof the renormalization map, and we compute the scalingbehaviour of the critical function of one-parameterfamilies of Hamiltonians, near rational frequencies. Forthe forced pendulum model, we find the same scaling lawfound for the standard map (Carletti and Laskar 2000Nonlinearity 13 2033). We discuss aconjecture on the link between the critical function ofvarious types of forced pendulum models, with the Brunofunction.
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