seminar: Hyperbolic Billiards and Ergodicity

speaker: Gianluigi Del Magno (Università di Pisa)

abstract: This talk concerns a class of Hamiltonian systems called billiards. A billiard in a domain Q of the Euclidean space R^{n} is the dynamical system generated by a point-particle moving freely inside Q, and being reflected elastically when it hits the boundary of Q. More specifically, I will consider hyperbolic billiards. These billiards are natural models for physical systems of colliding particles; they include classical models like hard balls systems and the Lorentz gas. The study of hyperbolic billiards started with the seminal works of Sinai and Bunimovich in the 60's and 70's. Since then, there has been an active research to generalize their results. In this talk, I will address the questions of the ergodicity and the construction of high-dimensional hyperbolic billiards. In the first part of the talk, I will give some background on billiards. Then, in the second part of the talk, I will report on 3 projects I have been working on recently. The first project concerns the ergodicity of hyperbolic billiards in the plane, the second is about stadium-billiards in R^{3}, and finally the third project is about a class of billiards in the plane modelling the motion of particles in nanostructures.

timetable:
Sat 1 Sep, 11:15 - 12:15, Lizzanello
<< Go back