Complexity of trajectories in rectangular billiards

Research output: Contribution to journalArticlepeer-review


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 (US)
Pages (from-to)43-56
Number of pages14
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Nov 1995
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Complexity of trajectories in rectangular billiards'. Together they form a unique fingerprint.

Cite this