The fractal dimensions of the spectrum of Sturm Hamiltonian

Qinghui Liu, Yanhui Qu, Zhiying Wen

Let $\alpha \in (0,1)$ be irrational and $[0;a_1,a_2,\cdots ]$ be the continued fraction expansion of $\alpha$. Let $H_{\alpha ,V}$ be the Sturm Hamiltonian with frequency $\alpha$ and coupling $V$, $Σ_{α…