4 problems

Let $H_{\lambda}^{(3)}$ be the three-dimensional Fibonacci Hamiltonian, and let $\operatorname{Sp}(H_{\lambda}^{(3)})$ denote its spectrum. Fibonacci spectrum components conjecture…

Let $H_{\lambda}$ be the one-dimensional Fibonacci Hamiltonian with coupling $\lambda$, and let $H_{\lambda}^{(d)}$ be its $d$-dimensional Fibonacci Hamiltonian. Write…

Fibonacci-spectrum monotonicity conjecture. The Hausdorff dimension $\mathbf{dim}_\mathrm{H}(\Sigma_\lambda)$ is a monotone function of the coupling constant $\lambda$.

Monotonicity conjecture. The function $d_\lambda$ is monotone in $\lambda$.