COMPLEXITY OF TRAJECTORIES IN RECTANGULAR BILLIARDS

Autor(en): BARYSHNIKOV, Y
Stichwörter: Physics; Physics, Mathematical
Erscheinungsdatum: 1995
Herausgeber: SPRINGER VERLAG
Journal: COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volumen: 174
Ausgabe: 1
Startseite: 43
Seitenende: 56
Zusammenfassung: 
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].
ISSN: 00103616

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