Explicit construction of gevrey quasi-periodic discrete schrödinger operators with cantor spectrum

Abstract

We construct 1-dim difference Schrödinger operators with a class of Gevrey potentials such that Cantor spectrum occurs together with the estimations of open spectral gaps . The proof is based on KAM and Moser-Pöschel argument .

In Chapters 3, 4, and 5, we presented more precise estimations