One-day Ergodic Theory Meeting

Programme:

14:00-15:00 Niloofar Kiamari (Loughborough)

15:00-16:00 Polina Vytnova (Warwick)

16:00-16:30 Break

16:30-17:30 Carlangelo Liverani (Rome)

Speaker: Niloofar Kiamari

Title: Locating Ruelle-Pollicott Resonances

Abstract: In this talk, we will present some new results regarding the spectrum of transfer operators associated to different classes of dynamical systems. Our goal is to obtain precise information on the discrete spectrum. We will describe a general principle which allows us to obtain substantial spectral information. We will then consider several settings where new information can be obtained using this approach, including affine expanding Markov maps, monotone maps, hyperbolic diffeomorphisms. (Joint work with: Oliver Butterley & Carlangelo Liverani.)

Speaker: Polina Vytnova

Title: A new approach to computing Lyapunov exponents

Abstract: Last year, in a joint work with M. Pollicott we have presented a new and remarkably efficient way of computing Hausdorff dimension of certain dynamically defined Cantor sets. Recently, we have extended this method to computing Lyapunov exponents of random matrix products under contraction on average hypothesis by Le Page. In the talk I am planning to give some theoretical background and to present several examples.

Speaker: Carlangelo Liverani

Title: Hyperbolic Billiards

Abstract: The study of the statistical properties of billiards has seen a rapid evolution in the last 25 years and many new ideas have been developed to further their study. Yet, there are many interesting models (such as open systems, time varying billiards and, most of all, the Random Lorentz gas) for which the current techniques are not optimal. I will first quickly describe the current state of the art in the study of hyperbolic billiards, and then I will discuss some recent development that attempt to address the aforementioned problems (work in collaboration with Mark Demers).