Meilleures approximations d'un élément du tore ² et géométrie de la suite des multiples de cet élément

ArticleOriginal scientific text

Title

Authors ¹

best simultaneous diophantine approximation, continued fraction, metric theory, Voronoï diagram, Rokhlin tower

[Ca] J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge Tracts in Math. and Math. Phys. 45, Cambridge Univ. Press, 1965.
[Ch] N. Chevallier, Distances dans la suite des multiples d'un point du tore à deux dimensions, Acta Arith. 74 (1996), 47-59.
[H-W] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford University Press, 1971.
[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.
[L2] J. C. Lagarias, Best simultaneous Diophantine approximations I. Growth rates of best approximations denominators, Trans. Amer. Math. Soc. 272 (1982), 545-554.
[L3] J. C. Lagarias, Best simultaneous Diophantine approximations II. Behavior of consecutive best approximations, Pacific J. Math. 102 (1982), 61-88.
[L4] J. C. Lagarias, Geodesic multidimensional continued fractions, Proc. London Math. Soc. (3) 69 (1994), 464-488.
[Sp] V. G. Sprindžuk, Metric Theory of Diophantine Approximations, V. H. Winston & Sons, Washington, D.C., 1979.
[Sz-Só] G. Szekeres and V. T. Sós, Rational approximation vectors, Acta Arith. 49 (1988), 255-261.