Georgia Institute of Technology College of Sciences

I will consider the long-time influence of deterministic and stochastic perturbations of dynamical systems and diffusion processes with a first integral . A diffusion process on the Reeb graph of the first integral determines the long-time behavior of the perturbed system. In particular, I will consider stochasticity of long time behavior of deterministic systems close to a system with a conservation law. Which of the invariant  measures of the non-perturbed system will be limiting for a given class of perturbations also will be discussed.