Spectrums Of Discrete Shrodinger Operators With Limit Periodic Potential

This paper is mainly devoted to some results about the Schrodinger op-erators with limit-periodic potentials, which generally comes form Avila, Damanik, Zheng Gan, Avron, Simon and Poschel. Generic potentials have Cantor spectrums, as the2nd chapter shows. In the3rd chapter, those who have absolutely continuous spectrum form a dense set. In case of zero measure spectrum and singular continuous spectrum, the conclusion are both "generic", which will be given in the4th and5th chapter re-spectively. In the6th chapter, there exist some special potentials which generate pure point spectrum. These results will be further considered in the7th chapter.