  In this paper, we analyze the adiabatic crossing of a resonance for
Hamiltonian systems when a double-resonance condition is satisfied by the
linear frequency at an elliptic fixed point. We discuss in detail the
phase-space structure on a class of Hamiltonians and area-preserving maps with
an elliptic fixed point in the presence of a time-dependent exciter. Various
regimes have been identified and carefully studied. This study extends results
obtained recently for the trapping and transport phenomena for periodically
perturbed Hamiltonian systems, and it could have relevant applications in the
adiabatic beam splitting in accelerator physics.
