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Tuesday 18 May 2021Transfer operators: the old, the new and the upcoming

Wael Bahsoun - University of Loughborough Meeting ID: 943 8343 7151 Password: 799310 13:30-14:30

Smooth ergodic theory aims to analyse the long-term statistics of chaotic dynamical systems. There are several analytic and probabilistic tools that are used to answer such questions. Each of these approaches has its advantages and its shortcomings, depending on the system under consideration. In this presentation, I will focus on transfer operator techniques and spectral methods, which are known to be very powerful when dealing with uniformly expanding, or uniformly hyperbolic systems. The first half of this talk will be rather elementary, aimed at non-experts, focusing on ideas behind this approach through simple, yet important examples. In the second half of the talk, I will discuss a recent joint work with C. Liverani, whose long-term goal is to provide a good spectral picture for piecewise hyperbolic systems with singularities (e.g. billiard maps). I will also discuss a recent joint work with F. Sélley on coupled map lattices.

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