A common model in physics is to replace a mechanical Hamiltonian system with a steep potential by an inertial motion in the corresponding domain with specular reflections at its boundary. This type of dynamics is named billiard motion. The most celebrated model of this kind is related to Boltzmann's hypothesis, in which molecules are replaced by hard spheres. When is such an approximation justified? What type of new dynamical phenomena arise when the approximation fails? In recent years we have developed a framework for dealing with such questions, mainly for two dimensional systems. I will survey these developments and some recent experiments in which our findings are observed.
This is a joint work with Dmitry Turaev.