3, Tereshchenkivska str., 01601, Kiev, Ukraine
Institute of Mathematics of Ukrainian National Academy of Sciences, Kiev
Albeverio S., Galperin G. A., Nizhnik I. L., Nizhnik L. P.
Generalized billiards inside an infinite strip with periodic laws of reflection along the strip's boundaries
2005, vol. 10, no. 3, pp. 285-306
A constructive description of generalized billiards is given, the billiards being inside an infinite strip with a periodic law of reflection off the strip's bottom and top boundaries. Each of the boundaries is equipped with the same periodic lattice, where the number of lattice's nodes between any two successive reflection points may be prescribed arbitrarily. For such billiards, a full description of the structure of the set of billiard trajectories is provided, the existence of spatial chaos is found, and the exact value of the spatial entropy in the class of monotonic billiard trajectories is found.