Exact logarithmic Hausdorff and capacity exponents of the non-Brjuno set

Let $\mathcal{N}$ be the set of non-Brjuno real numbers. We determine the exact critical exponent of $\mathcal{N}$ for both logarithmic Hausdorff measure and logarithmic capacity. For the gauges $h_δ(r)=(\log(1/r))^{-δ}$, the critical exponent is $2$: the $h_δ$-Hausdorff measure is infinite locally