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arXiv · 2005.02128

Winning property of badly approximable points on curves

Victor Beresnevich·Erez Nesharim·Lei Yang
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Abstract

In this paper we prove that badly approximable points on any analytic non-degenerate curve in $\mathbb{R}^n$ is an absolute winning set. This confirms a key conjecture in the area stated by Badziahin and Velani (2014) which represents a far-reaching generalisation of Davenport's problem from the 1960s. Amongst various consequences of our main result is a solution to Bugeaud's problem on real numbers badly approximable by algebraic numbers of arbitrary degree. The proof relies on new ideas from fractal geometry and homogeneous dynamics.

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Victor Beresnevich, Erez Nesharim, Lei Yang. 2020-05-05. Winning property of badly approximable points on curves. https://arxiv.org/abs/2005.02128

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