### Abstract

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].

Original language | English |
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Pages (from-to) | 43-56 |

Number of pages | 14 |

Journal | Communications in Mathematical Physics |

Volume | 174 |

Issue number | 1 |

DOIs | |

Publication status | Published - Nov 1 1995 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Yu. Baryshnikov, B. (1995). Complexity of trajectories in rectangular billiards.

*Communications in Mathematical Physics*,*174*(1), 43-56. https://doi.org/10.1007/BF02099463