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.

Analysis of adiabatic trapping phenomena for quasi-integrable area-preserving maps in the presence of time-dependent exciters.

In this paper, results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps and Hamiltonians with a time-dependent exciter are presented and discussed in detail. The applicability of the results about trapping efficiency for Hamiltonian systems to the maps considered is proven by using perturbation theory. This makes possible to determine explicit scaling laws for the trapping properties.