Rankin Lecture: Billiards

Carlos Matheus Silva Santos (CNRS, Paris)

Tuesday 18th February 16:00-17:00 Maths and Stats Building, Room 116

Abstract

Dynamical billiards were designed to serve as simpler models for intricate phenomena in Statistical Mechanics. Nevertheless, the body of research developed over the last 100 years taught us that the family of dynamical billiards is rich enough to exhibit all complicated behaviours (elliptic, parabolic and hyperbolic) described by the modern theory of Dynamical Systems. 

In this talk, after briefly recalling the link between dynamical billiards and Lorentz ideal gases in Statistical Mechanics, we will discuss billiards on ellipses, billiards on rational polygons, and Sinai billiards as an excuse to make a tour around the theories of elliptic, parabolic and hyperbolic systems. 

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