Chaotic Billiards
Billiards are mathematical models for many physical phenomena where one or more particles move in a container and collide with its walls and/or with each other. The dynamical properties of such models are determined by the shape of the walls of the container, and they may vary from completely regular (integrable) to fully chaotic. The most intriguing, though least elementary, are chaotic billiards. They include the classical models of hard balls studied by L. Boltzmann in the nineteenth century, the Lorentz gas introduced to describe electricity in 1905, as well as modern dispersing billiard tables due to Ya. Sinai.