Diophantine approximations and directional discrepancy of rotated lattices (Q2790611)
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scientific article; zbMATH DE number 6551081
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Diophantine approximations and directional discrepancy of rotated lattices |
scientific article; zbMATH DE number 6551081 |
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Diophantine approximations and directional discrepancy of rotated lattices (English)
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7 March 2016
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Diophantine approximation
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geometric measure theory
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asymptotic behavior
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directional discrepancy
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The authors study the following question related to Diophantine approximations and geometric measure theory: for a given set \(\Omega\) find \(\alpha\) such that \(\alpha-\theta\) has bad Diophantine properties simultaneously for all \(\theta\in \Omega\).NEWLINENEWLINEThis paper provide several methods, which yield different answers in terms of the metric entropy of \(\Omega\) and considered various examples. Furthermore, these results are applied to explore the asymptotic behavior of the directional discrepancy with respect to rectangles rotated in certain sets of directions.
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