Sydney Dynamics Group Seminar: Corinna Ulcigrai, University of Zurich -- Sydney Dynamics group Seminar

Seminar : Sydney Dynamics group Seminar.  
Day/time : Thursday, July 23 at 4:00 PM.
Location : SMRI seminar room (A12 Macleay Room 301).  
Speaker : Corinna Ulcigrai, University of Zurich.  

Title: Infinite Periodic Polygonal Billiards 

Abstract: Mathematical billiards provide interesting toy models of chaotic behaviour; 
billiards in polygonal tables, in particular, provide fundamental examples of slowly 
chaotic (zero-entropy) dynamical systems.  In this talk, we will focus on examples of 
infinite periodic planar polygonal billiards.  Notable physical motivations for studying 
such flows arise, for example, from the Ehrenfest (wind-tree) model and from systems 
of Eaton lenses.  

While the fine chaotic properties of billiards in bounded rational polygons (whose
angles are rational multiples of \pi are well understood, thanks to their connection
with flows on compact surfaces obtained by "unfolding" the billiard, many questions
remain open when both the billiard and the unfolded surface are infinite.  

We will present an overview of results and open problems in the periodic setting, with
particular emphasis on ergodicity.  We will also indicate how ergodicity is related to
phenomena such as deviations of ergodic integrals and "deterministic" random walks.