Dynamical Properties of SDEs with Shear

In this talk I will study the stochastic flow induced by planar stochastic differential equations in which the radial part of the drift term depends on the distance to the origin ("shear"). In particular I will derive tight conditions under which the flow is or is not strongly complete, does or does not admit a pull-back atractor and under which strong synchronization does or does not occur. Many of the methods used are new and could be applicable to larger classes of S(P)DE.

Most of the results are based on ongoing joined work with Maximilian Engel and Michael Scheutzow.