Statistical properties of randomly perturbed dynamical systems

The study of statistical properties in dynamical systems is currently one of the most active branches of research in ergodic theory. For deterministic dynamical systems, such properties have been established for various classes of systems, including the famous Lorenz attractor. The goal of the project is to investigate how much of such properties persist when the system is subject to random perturbations, and how the statistics of the randomly perturbed system can be approximated via the statistics of the unperturbed one.