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arXiv · 1610.01870

A Shrinking Target Problem with Target at Infinity in Rank One Homogeneous Spaces

Cheng Zheng
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Abstract

In this paper, we give a definition of Diophantine points of type $γ$ for $γ\geq0$ in a homogeneous space $G/Γ$, and compute the Hausdorff dimension of the subset of points which are not Diophantine of type $γ$ when $G$ is a semisimple Lie group of real rank one. We also deduce a Jarník-Besicovitch Theorem on Diophantine approximation in Heisenberg groups.

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Cheng Zheng. 2019-06-11. A Shrinking Target Problem with Target at Infinity in Rank One Homogeneous Spaces. https://doi.org/10.1007/s00605-019-01309-2

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