14:00 – 15:00
Mark Holland (University of Exeter): On Extremes, recurrence and record events in dynamical systems
For dynamical systems we discuss the statistics of extremes, namely the statistical limit laws that govern the process $M_{n}=max{X_1,X_2,ldots,X_n}$ , where $X_i$ correspond to a stationary time series of observations generated by the dynamical system. We discuss extreme statistics for a range of examples of interest to those working in ergodic theory and chaotic dynamical systems. In a work in progress, we discuss almost sure growth rates of $M_n$, and the statistics of records: namely the distribution of times $n$ such that $X_{n}=M_n$.
15:00 – 16:00
Mike Todd (University of St. Andrews): Dynamical systems with holes: slow mixing cases
Fernandez and Demers studied the statistical properties of the Manneville-Pomeau map with the physical measure when a hole is put in the system, overcoming some of the problems caused by subexponential mixing. I’ll discuss the same setup, but with a class of natural equilibrium states. We find conditionally invariant measures and give precise information on the transitions between the fast exponentially mixing, the slow exponentially mixing and the subexponentially mixing phases. This is joint work with Mark Demers.