Research Summary

My work focusses on the effects of small noisy perturbations on dynamical systems. Small thermal noise is present in most physical systems. It may also be used as a mathematical technique to model phenomena below the scale of interest. Small noise in a sense "regularizes", and in many cases allows one to asymptotically identify robust structures and features of dynamical systems. This is of particular interest in the analysis of bifurcations, where dominant dynamics change. The effect of small noise is often to identify natural ways in which real systems effect transitions between different types of behaviors.

The picture above is a Hamiltonian with a flat region. The figure at right is the reduction of the state space by chain equivalence of the symplectic gradient flow. Chain equivalence is the correct framework to carry out certain stochastic averaging problems.