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arxiv 2307.10109 v1 pith:4OIYHZQ4 submitted 2023-07-19 math.NT math.DS

Victor Beresnevich , Shreyasi Datta , Anish Ghosh , Benjamin Ward This is my paper · ORCID
classification math.NTmath.DS
keywords diophantineapproximableapproximationapproximationsbadlyframeworkmeasurepoints
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abstract

In this paper we develop a general framework of badly approximable points in a metric space $X$ equipped with a $\sigma$-finite doubling Borel regular measure $\mu$. We establish that under mild assumptions the $\mu$-measure of the set of badly approximable points is always zero. The framework can be applied to a variety of settings in Diophantine approximation and dynamical systems, which we also consider, including weighted and $S$-arithmetic Diophantine approximations, Diophantine approximation on manifolds and intrinsic approximations on fractals.

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Cited by 1 Pith paper

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  1. A note on limsup sets of annuli

    math.NT 2025-02 reject novelty 6.0 of 10

    The paper proves Jarnik-Besicovitch-type Hausdorff dimension formulas for limsup sets of annuli around rational points, including rectangular and norm-difference annuli.

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