Justification

In the year 1900 at the International Mathematical Congress the famous
mathematician, David Hilbert, included into his celebrated 23 problems the
sixth one titled Mathematical Treatment of the Axioms of Physics". Hilbert
wrote:

"*It is very desirable that the discussion of the foundations of
mechanics be taken up by mathematicians also. Thus, Boltzmann's work on the
principles of mechanics suggests the problem of developing mathematically the
limiting processes, there merely indicated, which lead from the atomistic view
to laws of motion of continua*".

More than 100 years later this problem and the Boltzmann works concerning foundations of statistical mechanics remains to be carefully understood. One of
the remarkable idea, which clarifies the main properties of many-particles
systems, goes back to rigorous version of Boltzmann's ergodic hypothesis
proposed by Ya.Sinai in his lecture at the International Congress of
Mathematicians in 1962 and know as Boltzmann-Sinai ergodic hypothesis. It
concerns the system of elastic hard balls, i.e. \textit{billiards}.

Analysis of the dynamics of billiard balls has been initiated by G.Coriolis,
who for the first time studied theoretically billiards in a plane. Later
J.Hadamard examined a question about the particle motion on a twisted surface
of negative curvature. However, the notion of billiards in the contemporary
sense is known since D.Bikhoff who studied a problem of the free motion of a
point particle (billiard ball) in a manifold. More complete investigation
related to the mixing property in hard ball systems has been carried out by
N.Krylov. However, thanks to the papers by Ya.G.Sinai a new epoch in the
rigorous analysis of billiards begun.

Nowadays, billiards became one of the most active and popular research areas.
They are a tempting topic of the theoretical physics and mathematics which
provide a fertile source of new ideas in geometry, hyperbolic systems, spectral
theory, mechanics, optics, statistical physics, astrophysics and other fields
of natural sciences.

The intent of the conference is

• to bring together the best scientists working, in particular, in mathematics,
theoretical and mathematical physics, who are doing new investigations in
billiard-type dynamical systems and non-equilibrium statistical mechanics,

• to talk about billiard works, and

• to report on new solutions and discoveries of fundamental problems in
statistical physics and dynamical systems.

The meeting will include plenary, invited, contributed and posters
presentations. It will be held in February 7--10, 2011, in Ubatuba --- a
beautiful place of the Brazilian Atlantic coast. The first International
School-Conference "Mathematics and Physics of Billiard-Like Systems"
(BILLIRDS'09) has occurred in Águas de Lindoia, Brazil, in February 2009.

A preliminary list of topics includes: many-particle classical systems,
Hamiltonian dynamics, billiards with fixed and time-dependent boundaries,
hyperbolic dynamical systems, applications. Other fields falling within the
general scope of the conference are welcome.

The Interdisciplinary Journal CHAOS will publish a focus issue on
Statistical Mechanics and Billiard-Type Dynamical Systems (tentatively
scheduled August--September 2011). This focus issue will consist of selected
papers from the BILLIARDS'2011 conference.