Complexity and growth for polygonal billiards

J. Cassaigne[1]; Pascal Hubert[1]; Serge Troubetzkoy[2]

  • [1] Institut de Mathématiques de Luminy, Case 907, 13288 Marseille Cedex 9 (France)
  • [2] Centre de Physique Théorique, Institut de Mathématiques de Luminy, Case 907, 13288 Marseille Cedex 9 (France)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 3, page 835-847
  • ISSN: 0373-0956

Abstract

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We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.

How to cite

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Cassaigne, J., Hubert, Pascal, and Troubetzkoy, Serge. "Complexity and growth for polygonal billiards." Annales de l’institut Fourier 52.3 (2002): 835-847. <http://eudml.org/doc/115996>.

@article{Cassaigne2002,
abstract = {We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.},
affiliation = {Institut de Mathématiques de Luminy, Case 907, 13288 Marseille Cedex 9 (France); Institut de Mathématiques de Luminy, Case 907, 13288 Marseille Cedex 9 (France); Centre de Physique Théorique, Institut de Mathématiques de Luminy, Case 907, 13288 Marseille Cedex 9 (France)},
author = {Cassaigne, J., Hubert, Pascal, Troubetzkoy, Serge},
journal = {Annales de l’institut Fourier},
keywords = {complexity; polygonal billiards; generalized diagonals; bispecial words},
language = {eng},
number = {3},
pages = {835-847},
publisher = {Association des Annales de l'Institut Fourier},
title = {Complexity and growth for polygonal billiards},
url = {http://eudml.org/doc/115996},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Cassaigne, J.
AU - Hubert, Pascal
AU - Troubetzkoy, Serge
TI - Complexity and growth for polygonal billiards
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 3
SP - 835
EP - 847
AB - We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.
LA - eng
KW - complexity; polygonal billiards; generalized diagonals; bispecial words
UR - http://eudml.org/doc/115996
ER -

References

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