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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.


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Grupo de Investigação em Sistemas Complexos e Dinâmica Não-linear - UNESP - Rio Claro - SP