Meilleures approximations d'un élément du tore 𝕋² et géométrie de la suite des multiples de cet élément

Nicolas Chevallier

Acta Arithmetica (1996)

  • Volume: 78, Issue: 1, page 19-35
  • ISSN: 0065-1036

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Nicolas Chevallier. "Meilleures approximations d'un élément du tore 𝕋² et géométrie de la suite des multiples de cet élément." Acta Arithmetica 78.1 (1996): 19-35. <http://eudml.org/doc/206930>.

@article{NicolasChevallier1996,
author = {Nicolas Chevallier},
journal = {Acta Arithmetica},
keywords = {best simultaneous diophantine approximation; continued fraction; metric theory; Voronoï diagram; Rokhlin tower; Voronoï diagrams},
language = {fre},
number = {1},
pages = {19-35},
title = {Meilleures approximations d'un élément du tore 𝕋² et géométrie de la suite des multiples de cet élément},
url = {http://eudml.org/doc/206930},
volume = {78},
year = {1996},
}

TY - JOUR
AU - Nicolas Chevallier
TI - Meilleures approximations d'un élément du tore 𝕋² et géométrie de la suite des multiples de cet élément
JO - Acta Arithmetica
PY - 1996
VL - 78
IS - 1
SP - 19
EP - 35
LA - fre
KW - best simultaneous diophantine approximation; continued fraction; metric theory; Voronoï diagram; Rokhlin tower; Voronoï diagrams
UR - http://eudml.org/doc/206930
ER -

References

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  1. [Ca] J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge Tracts in Math. and Math. Phys. 45, Cambridge Univ. Press, 1965. 
  2. [Ch] N. Chevallier, Distances dans la suite des multiples d'un point du tore à deux dimensions, Acta Arith. 74 (1996), 47-59. 
  3. [H-W] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford University Press, 1971. 
  4. [L1] J. C. Lagarias, Some new results in simultaneous Diophantine approximation, in: Proc. of the Queen's Number Theory Conference 1979, P. Ribenboim (ed.), Queen's Papers in Pure and Appl. Math. 54, 1980, 453-474. 
  5. [L2] J. C. Lagarias, Best simultaneous Diophantine approximations I. Growth rates of best approximations denominators, Trans. Amer. Math. Soc. 272 (1982), 545-554. Zbl0495.10021
  6. [L3] J. C. Lagarias, Best simultaneous Diophantine approximations II. Behavior of consecutive best approximations, Pacific J. Math. 102 (1982), 61-88. Zbl0497.10025
  7. [L4] J. C. Lagarias, Geodesic multidimensional continued fractions, Proc. London Math. Soc. (3) 69 (1994), 464-488. Zbl0813.11040
  8. [Sp] V. G. Sprindžuk, Metric Theory of Diophantine Approximations, V. H. Winston & Sons, Washington, D.C., 1979. 
  9. [Sz-Só] G. Szekeres and V. T. Sós, Rational approximation vectors, Acta Arith. 49 (1988), 255-261. Zbl0637.10024

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