Spectral properties of discrete schrodinger operator with quasi-periodically recurrent potential

In this paper, we study discrete Schrodinger operators with sparse barrier type potentials, and investigate a-continuity or a-singularity of the spectral measure by estimating the upper and lower bounds of the Hausdorff dimensions of its spectrum. Furthermore, we introduce quasi- periodically recurrent potentials and we estimate the Hausdorff dimensions of the spectrum, using the constants associated with continued fraction expansion of irrational frequencies.