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

Abstract

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. These findings represent a generalization of previous results obtained for the case of quasi-integrable maps with parametric modulation, as well as an extension of the work by Neishtadt etal. [Regul. Chaotic Dyn. 18, 686 (2013)10.1134/S1560354713060087] on a restricted class of quasi-integrable systems with time-dependent exciters.