Duke Mathematical Journal
- Duke Math. J.
- Volume 165, Number 12 (2016), 2273-2329.
Hausdorff dimension of singular vectors
We prove that the set of singular vectors in , , has Hausdorff dimension and that the Hausdorff dimension of the set of -Dirichlet improvable vectors in is roughly plus a power of between and . As a corollary, the set of divergent trajectories of the flow by acting on has Hausdorff codimension . These results extend the work of the first author.
Duke Math. J. Volume 165, Number 12 (2016), 2273-2329.
Received: 20 February 2014
Revised: 13 September 2015
First available in Project Euclid: 6 September 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11J13: Simultaneous homogeneous approximation, linear forms 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
Secondary: 37A17: Homogeneous flows [See also 22Fxx]
Cheung, Yitwah; Chevallier, Nicolas. Hausdorff dimension of singular vectors. Duke Math. J. 165 (2016), no. 12, 2273--2329. doi:10.1215/00127094-3477021. https://projecteuclid.org/euclid.dmj/1473186401