Justification

Systems of the billiard type represent one of the most popular and best investigated class of hyperbolic dynamical systems. The billiard problem is a fascinating subject providing a fertile source of new problems such as conjecture testing in dynamics, geometry, theoretical and mathematical physics, mathematics, optics, thermodynamics, spectral theory, etc. Thus, since the early beginnings of the study of classical and quantum chaos, billiards have been used as a paradigm.

Billiards correspond to one of the best understood classes of dynamical systems that demonstrate a broad variety of behaviours including passages from integrable to mixed form and eventually to an entire chaotic dynamics. In fact, several key properties of chaotic dynamics were first observed and demonstrated for billiards. Many popular models of statistical mechanics, e.g., the Lorenz gas, the hard sphere (Boltzmann and Sinai) gas, etc., can be reduced to billiards. Moreover, examples of some formal models of the billiard type exhibit a wide class of behaviours with a number of new unexpected features. Such fundamental notions as Boltzmann ergodic hypothesis, Fermi acceleration, Maxwell's demon, Hamiltonian systems with divided phase space, the Riemann zeta-function, etc. obtain natural physical realizations.

The aim of this school-conference is to bring together renowned scientists in the field, leaving enough time and opportunity for fruitful discussions among the participants.