Localizing transport barriers in degenerate 3/2 D.O.F. Hamiltonian systems with applications to magnetic confinement fusion

The existence of transport barriers in 3/2 degrees of freedom degenerate Hamiltonian systems is studied using the associated stroboscopic maps. For small enough amplitudes of the perturbations, a transport barrier (formed by infinitely many invariant rotational circles) is proven to exist and to form in the degenerate annulus. These results are applied to Hamiltonian models which describe some magnetic configurations in tokamak plasmas.