Perturbations of Collective Hamiltonian Systems generated by Lie Algebra contractions

Abstract

In this article we study perturbed Hamiltonian dynamics in the class of collective Hamiltonian systems associated to Lie algebra Hamiltonian actions. For perturbations of collective systems generated by contractions of a compact Lie algebra \U0001d524 into a limiting algebra \U0001d5240, we give general conditions to transform such perturbations coming from deformations of the action into perturbations produced by corrections in the energy function of the collective system associated to the action by the limiting Lie algebra g0. We give an application to perturbations of collective systems generated by contraction of so(4) into e(3).