Thursday February 22, 4:00PM, Herman Brown 227
Given a dynamical system having a physical measure, the time averages of continuous functions on orbits of a positive volume subset of points converge to the space average with respect to the physical measure. A bound for large deviations gives the asymptotic measure of the set of points whose time averages stay away from the space average for many iterates. We show that the volume of this subset of points decays exponentially fast with the number of iterates for non-uniformly expanding transformations with singularities/criticalities and for special flows build over these transformations which model, in particular, the flow of the Lorenz equations.