Complexity of trajectories in rectangular billiards

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)43-56
Number of pages14
JournalCommunications in Mathematical Physics
Volume174
Issue number1
DOIs
StatePublished - Nov 1 1995
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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