Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential

Abstract

In this article, we prove a reducibility result for the linear Schrödinger equation on a Zoll manifold with quasi-periodic in time pseudo-differential perturbation of order less than or equal to 1/2. As far as we know, this is the first reducibility result for an unbounded perturbation on a compact manifold different from the torus.