Pure Maths Colloquium: Natalia Jurga

Let \(f:I \mapsto I\) be a map of an interval equipped with an ergodic measure \(\mu\). In this talk we will introduce and discuss the cover time of the system \((f,\mu)\). This roughly speaking describes the asymptotic rate at which orbits become dense in the state space \(I\), or in other words, what is the expected amount of time one has to wait for an orbit to reach a given density in the state space. We will discuss how one can combine probabilistic tools and operator theoretic methods in order to estimate the expected cover time in terms of the local scaling properties of the measure \(\mu\). This is based on joint work with Mike Todd.