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

TL;DR

This paper investigates adiabatic trapping in quasi-integrable area-preserving maps with time-dependent exciters, deriving explicit scaling laws and extending previous results to a broader class of systems using perturbation theory.

Contribution

It introduces new results on trapping phenomena in quasi-integrable maps with time-dependent exciters, generalizing prior work and providing explicit scaling laws.

Findings

Derived explicit scaling laws for trapping properties.

Extended previous results to broader classes of maps.

Validated applicability of Hamiltonian system results to these maps.

Abstract

In this paper, new results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps 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 allows determining 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 \textit{et al.} on a restricted class of quasi-integrable systems with time-dependent exciters.