Complexity of trajectories in rectangular billiards

Baryshnikov Yu. Baryshnikov

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


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 languageEnglish
Pages (from-to)43-56
Number of pages14
JournalCommunications in Mathematical Physics
Issue number1
Publication statusPublished - Nov 1 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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