Title: Shadowing and Weak Approximation for Dynamical Systems
Abstract: Consider simulating a dynamical system starting from random initial conditions. If the system is chaotic then numerical simulations of individual realizations are extremely inaccurate. Surprisingly, computed trajectories often appear to be accurate in the weak sense, that is, when expectations of functionals of the trajectories are considered. I will show how this phenomenon is equivalent to a concept from dynamical system known as shadowing. The key result is the equivalence proof is a version of the Strassen-Dudley theorem for coupling random variables that are close in theweak sense.