# Tuesday 22 Feb 2022: Cover times for dynamical systems

### Natalia Jurga - University of St Andrews

LSI Seminar Room B 13:30-14:30

Given an interval map $f:I \to I$ and ergodic measure $\mu$ we study the asymptotic expected behaviour of the cover time: the rate at which orbits become dense in the state space $I$. We will see how this can be studied through the lens of dynamical systems with holes. Using transfer operator tools for such systems and inducing techniques, we obtain an asymptotic formula for the expected cover time for a wide class of uniformly hyperbolic and non-uniformly hyperbolic interval maps. This is joint work with Mike Todd.