Santiago Dynamical Systems Seminar “Equidistribution in dynamical systems”

Abstract: Given an ergodic dynamical system, the proportion of times a typical orbit spends in a given set  is asymptotically the measure of that set.  We can quantify how close an orbit is to this equidistribution by taking δ > 0 and ε > 0 and seeing how long it takes for the orbit to have hit every δ-ball a proportion of the time greater than (1 – ε) times the measure of that ball.

Computing the expected value of such a `blanket time' is a classical problem in probability, particularly for random walks on finite graphs.  Here we give asymptotics for the expectation for small δ, ε, a type of quantitative equidistribution, for a class of dynamical systems.  This is joint work with Natalia Jurga.

Speaker: Mike Todd (University of St Andrews)