Mark Freidlin, University of Maryland

*Title: *Long-Time Influence of Small Perturbations

*Abstract*: Long-time influence of small deterministic and stochastic perturbations can be described as a motion on the simplex of invariant probability measures of the non-perturbed system. I will demonstrate this general approach in the case of perturbations of a stochastic system with multiple stationary regimes. If the system has a first integral, the long–time behavior of the perturbed system, in an appropriate time scale, can be described by a motion on the Reeb graph of the first integral. This is a modified (because of the interior vertices of the Reeb graph) averaging-principle-type result. If the non-perturbed stochastic system has just a finite number of ergodic invariant probability measures, the long-time behavior is defined by limit theorems for large deviations.