K. Rakhimov

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 $h_\delta(r)=(\log(1/r))^{-\delta}$, the critical exponent is $2$: the $h_\delta$-Hausdorff measure is infinite locally for $...