Qing-Hui LIU, Zhi-Ying WEN
Hausdorff dimension of spectrum of one-dimensional Schr\"odinger operator with Sturmian potentials
(354K, Postscript)

ABSTRACT.  Let $\beta\in(0,1)$ be an irrational, and $[a_1,a_2,\cdots]$ the 
continued fraction expansion of $\beta$. Let $H_\beta$ be the 
one-dimensional Schr\"odinger operator with Sturmian potentials. 
We prove that if the potential strength $V>20$, then the Hausdorff 
dimension of the spectrum $\sigma(H_\beta)$ is strictly great than 
zero for any irrational $\beta$, and is strictly less than $1$ if 
and only if $\liminf\limits_{k\rightarrow\infty}(a_1 a_2 \cdots 
a_k)^{1/k}<\infty$.