A METAPHOR FOR ADIABATIC EVOLUTION TO SYMMETRY

In this paper we study a Hamiltonian system with a spatially asymmetri c potential. We are interested in the effects on the dynamics when the potential becomes symmetric slowly in time. We focus on a highly simp lified nontrivial model problem (a metaphor) to be able to pursue expl icit calculations as far as possible. Using the techniques of averagin g and adiabatic invariants, we are able to study all bounded solutions , which reveals significant asymmetric dynamics even when the asymmetr ic contributions to the potential have become negligibly small.