To a trajectory of the billiard in a cube we assign its symbolic trajectory-the sequence of numbers of coordinate planes, to which the faces met by the trajectory are parallel. The complexity of the trajectory is the number of different words of length n occurring in it. We prove that for generic trajectories the complexity is well defined and calculate it, confirming the conjecture of Arnoux, Mauduit, Shiokawa and Tamura [AMST].
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics