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Geométrie des suites de Kronecker

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Abstract

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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  1. Université de haute Alsace, 4, rue des frères Lumières, 68093, Mulhouse, France

    Nicolas Chevallier

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  1. Nicolas Chevallier
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Chevallier, N. Geométrie des suites de Kronecker. Manuscripta Math 94, 231–241 (1997). https://doi.org/10.1007/BF02677849

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  • DOI: https://doi.org/10.1007/BF02677849

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