Abstract: Given a family of rational maps, each with an assigned probability, we can form a stochastic dynamical system by allowing our system to randomly iterate according to the given probability of each map. When studying the dynamics of a single rational map, one of the key ideas is to break the plane up into a region where the iterates behave regularly in some fashion (the Fatou set) and a complementary set where the iterates behave chaotically (the Julia set). One can then prove an equidistribution theorem for (pre)periodic points or, more generally, for points of low dynamical height along a certain canonical measure associated to the Julia set. In this talk we will explore recent analogous results, including a new equidistribution theorem on random backwards orbits, for the arithmetic of stochastic dynamical systems. (Joint work with John Doyle and Bella Tobin.)
To add/edit talks, please log in on the department web page, then return to Announce. Alternatively if you know the Announce
username/password, click the link below: