Billiard complexity in the hypercube

Nicolas Bedaride[1]; Pascal Hubert[2]

  • [1] Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d’Analyse Topologie et Probabilités Av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France)
  • [2] Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d’Analyse Topologie et Probabilités av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 3, page 719-738
  • ISSN: 0373-0956

Abstract

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We consider the billiard map in the hypercube of ℝ d . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that n 3 d - 3 is the order of magnitude of the complexity.

How to cite

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Bedaride, Nicolas, and Hubert, Pascal. "Billiard complexity in the hypercube." Annales de l’institut Fourier 57.3 (2007): 719-738. <http://eudml.org/doc/10239>.

@article{Bedaride2007,
abstract = {We consider the billiard map in the hypercube of $\mathbb\{R\}^d$. We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that $n^\{3d-3\}$ is the order of magnitude of the complexity.},
affiliation = {Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d’Analyse Topologie et Probabilités Av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France); Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d’Analyse Topologie et Probabilités av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France)},
author = {Bedaride, Nicolas, Hubert, Pascal},
journal = {Annales de l’institut Fourier},
keywords = {Symbolic dynamic; billiard; words; complexity function; symbolic dynamic},
language = {eng},
number = {3},
pages = {719-738},
publisher = {Association des Annales de l’institut Fourier},
title = {Billiard complexity in the hypercube},
url = {http://eudml.org/doc/10239},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Bedaride, Nicolas
AU - Hubert, Pascal
TI - Billiard complexity in the hypercube
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 3
SP - 719
EP - 738
AB - We consider the billiard map in the hypercube of $\mathbb{R}^d$. We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that $n^{3d-3}$ is the order of magnitude of the complexity.
LA - eng
KW - Symbolic dynamic; billiard; words; complexity function; symbolic dynamic
UR - http://eudml.org/doc/10239
ER -

References

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