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1 September 2016 Hausdorff dimension of singular vectors
Yitwah Cheung, Nicolas Chevallier
Duke Math. J. 165(12): 2273-2329 (1 September 2016). DOI: 10.1215/00127094-3477021

Abstract

We prove that the set of singular vectors in Rd, d2, has Hausdorff dimension d2d+1 and that the Hausdorff dimension of the set of ε-Dirichlet improvable vectors in Rd is roughly d2d+1 plus a power of ε between d2 and d. As a corollary, the set of divergent trajectories of the flow by diag(et,,et,edt) acting on SLd+1(R)/SLd+1(Z) has Hausdorff codimension dd+1. These results extend the work of the first author.

Citation

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Yitwah Cheung. Nicolas Chevallier. "Hausdorff dimension of singular vectors." Duke Math. J. 165 (12) 2273 - 2329, 1 September 2016. https://doi.org/10.1215/00127094-3477021

Information

Received: 20 February 2014; Revised: 13 September 2015; Published: 1 September 2016
First available in Project Euclid: 6 September 2016

zbMATH: 1358.11078
MathSciNet: MR3544282
Digital Object Identifier: 10.1215/00127094-3477021

Subjects:
Primary: 11J13, 11K55
Secondary: 37A17

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 12 • 1 September 2016
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