Randomly-Perturbed Hamiltonian Systems

 

Abstract

We discuss the effects of noise upon Hamiltonian systems, focussing upon some notions of dimensional reduction for such systems.  In simple cases, this is stochastic averaging as was studied by Khasminskii in the 1960's.  More complicated problems lead to processes on graphs, as was understood by Freidlin and Wentzell and Weber.  Degeneracies may yield processes on stratified spaces.  We discuss some general ideas behind these problems and identify some open areas of research.