A fresh look at the shadowing of pseudo-trajectories

The problem of shadowing of pseudo-trajectories was inspired by the classical results of D.V.Anosov on the robustness of uniformly hyperbolic systems. The main difficulty here lies in the analysis of infinitely many (in time) perturbations of the system. I will discuss a new approach to the shadowing problem that allows us to overcome this difficulty and expands dramatically its applicability to irreversibleand discontinuous systems, as well as to more general types of perturbations (for example, Gaussian).