2 problems

For an irrational $\alpha\in(0,1)$, let $\sigma_{\lambda,\alpha}$ denote the corresponding Sturmian spectrum and let $\dim_H$ denote Hausdorff dimension. Small-coupling continuity…

Small-coupling constancy conjecture. For $\lambda>0$ sufficiently small, the map $\alpha\mapsto \dim_H\sigma_{\lambda,\alpha}$ is $\alpha$-almost everywhere constant with respect t…