Analysis of double-resonance crossing in adiabatic trapping phenomena for quasi-integrable area-preserving maps with time-dependent exciters

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.