Dr. Richard Sowers, Department of Mathematics at University of Illinois at Urbana-Champaigny

A propagation-of-chaos type result in stochastic averaging

Stochastic averaging goes back to Khasminskii in the 1960's. The standard result is that, given a separation of scales, one can find effective dynamics for slow components. We investigate the motion of two particles in such a system, in particular in a randomly-perturbed twist map.  The nub of the issue is how two points escape from a 1-1 resonance zone. Results of Pinsky and Wihstutz indicate that there is a third scale at work, which we can use to study the escape from resonance.