manuscripta mathematica

, Volume 94, Issue 1, pp 231–241 | Cite as

Geométrie des suites de Kronecker

  • Nicolas Chevallier


Let Θ be a element of the d-dimensional torus\(\mathbb{T}\) d andτ the translationτ(x)=x + Θ. When d=1 there existe some partitions of\(\mathbb{T}\) 1 which are associated withτ. We prove the existence of partitions of\(\mathbb{T}\) d which enjoyed the same kind of properties and whose elements (A i ) i≤n are convex polytopes. We also give a lower bound for the isotropic discrepancy of the sequence (nΘ) nεℕ.


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Nicolas Chevallier
    • 1
  1. 1.Université de haute AlsaceMulhouseFrance

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