Natella O'Bryant (UCI)
"A noisy problem with a degenerate Hamiltonian and multiple time scales."
We consider a two-dimensional weakly dissipative dynamical system with time-periodic coefficients. Their time average is governed by a degenerate Hamiltonian whose set of critical points has an interior. The dynamics of the system is studied in the presence of three time scales. Using the martingale problem approach and separating the involved time scales, we average the system to show convergence to a Markov process on a stratified space. The corresponding strata of the reduced space are a two-sphere, a point, and a line segment. Special attention is given to the domain of the limiting generator, including the analysis of the gluing conditions at the point where the strata meet. The gluing conditions resulting from the hierarchy of the time scales are similar to the conditions on the domain of skew Brownian motion.