seminar: Ergodic semi-focusing billiards
speaker: Gianluigi Del Magno (Università di Pisa)abstract: A billiard on a planar domain Q (billiard table) is a mechanical system consisting of a point-particle which moves freely at unit speed inside Q and bounces off the boundary of Q elastically (the angle of incidence equals the angle of reflection).
Billiards arise naturally as models in statistical mechanics (hard-ball systems, Lorentz gas, etc.). Besides this fact, billiards are interesting dynamical systems because they show a variety of dynamics ranging from integrable behavior (e.g. a billiard inside an ellipse) to chaotic behavior (e.g. a billiard on a stadium-like domain).
In this talk, after reviewing general facts about billiards, I will focus on a class hyperbolic billiards called semi-focusing, their billiard table being bounded by segments and "focusing" curves. The prototype of these billiards is the stadium introduced together with other semi-focusing billiards by Bunimovich in the late 70's. Bunimovich's billiards are hyperbolic and ergodic. Their peculiarity is that the focusing curves are arcs of circles. More recently, several authors (Wotjkowski, Markarian, Bunimovich and Donnay) discovered new focusing curves that can be used to construct hyperbolic semi-focusing billiards. In the second part of this talk, I will discuss a joint work with R. Markarian, in which we proved that these new hyperbolic billiards are ergodic.
timetable:
Wed 15 Dec, 14:30 - 15:30, Sala Conferenze Centro De Giorgi
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