Dynamical Systems Seminar

One of the most efficient tools for studying the mixing rates of certain classes of dynamical systems is through Young towers: if a given system admits a tower whose tail of recurrence times decays at a given speed, then that system admits an absolutely continuous ergodic measure (physical measure) with mixing rate of the same order. In this talk we characterize the physical measures which are projected from towers. In a second step we show that if a physical measure has a certain mixing rate, then that measure comes from a Young tower with the tail of recurrence times decaying at related speed.