2 problems

Let $B_\sigma:[0,1]\to\mathbb R$ be the $\sigma$-Brjuno function, and let $\eta_n=(\sqrt{n^2+4}-n)/2$ be the $n$-th fixed point of the Gauss map. For each $n\in\mathbb N$, consider…

Let $B_1$ denote the classical Brjuno function, let $\mathcal{M}$ be the set of its local minima, and let $\mathcal{N}$ be the set of noble numbers, namely the numbers whose regular…