Billiards: models with chaotic dynamics. (Spanish) Zbl 1060.37032
This nice expository article gives account of the Boltzmann’s ergodic hypothesis and gas model in terms of modern ergodic theory. Different planar billiards and their chaotic properties are discussed. The ergodic-theoretic history behind the formulation of the Boltzmann-Sinai ergodic conjecture is related, and the Sinai billiard model for hard balls gases is described. Basics from hyperbolicity and Pesin theory are reviewed with an eye on the ergodicity problem of semi-dispersing billiards. Finally, recent progress on the full Boltzmann-Sinai conjecture – still open – are summarized.
There is an excellent related survey by L.-S. Young in [Mazur, B. (ed.) et al., Current developments in mathematics, 1998, Proceedings of the conference, Cambridge, MA, USA, 1998, Somerville, MA: International Press, 237–278 (1999; Zbl 1003.37023)].
There is an excellent related survey by L.-S. Young in [Mazur, B. (ed.) et al., Current developments in mathematics, 1998, Proceedings of the conference, Cambridge, MA, USA, 1998, Somerville, MA: International Press, 237–278 (1999; Zbl 1003.37023)].
Reviewer: José-Manuel Rey (Madrid)
MSC:
37D50 | Hyperbolic systems with singularities (billiards, etc.) (MSC2010) |
37A60 | Dynamical aspects of statistical mechanics |
37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
82C40 | Kinetic theory of gases in time-dependent statistical mechanics |