Dynamics of geodesic flows with random forcing on Lie groups with left-invariant metrics

Stochastics Seminar
Thursday, April 7, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 006
University of Minnesota, Twin Cities
Motivated by problems in turbulent mixing, we consider stochastic perturbations of geodesic flow for left-invariant metrics on finite-dimensional Lie groups. We study the ergodic properties and provide criteria that ensure the Hormander condition for the corresponding Markov processes on phase space. Two different types of models are considered: the first one is a classical Langevin type perturbation and the second one is a perturbation by a “conservative noise”. We also study an example of a non-compact group. Joint work with Vladimir Sverak.