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