Hausdorff dimension and uniform exponents in dimension two

Yann Bugeaud, Yitwah Cheung, Nicolas Chevallier

In this paper we prove the Hausdorff dimension of the set of (nondegenerate) singular two-dimensional vectors with uniform exponent $\mu$ $\in$ (1/2, 1) is 2(1 -- $\mu$) when $\mu$ $\ge$…