Cristel Chandre, Pierre Moussa
Scaling law for the critical function of an approximate renormalization
(188K, Postscript)
ABSTRACT. 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.