Geometry and dynamics of billiards in symmetric phase space
  The billiard problem of statistical physics is considered in a new geometric approach with a symmetric phase space. The structure and topological features of typical billiard phase portrait are defined. The connection between geometric, dynamic and statistic properties of smooth billiard is established. Other directions of the theory on development are pointed out. 
Sergey V. Naydenov, Vladimir V. Yanovsky