Reducibility of Schr\"odinger equation on a Zoll manifold with unbounded potential

TL;DR

This paper proves a reducibility result for the linear Schrödinger equation on Zoll manifolds with unbounded, quasi-periodic perturbations, marking a novel advancement in non-integrable linear systems.

Contribution

It establishes the first reducibility result for an unbounded perturbation of a non-integrable linear Schrödinger system on Zoll manifolds.

Findings

Proves reducibility for Schrödinger equations with unbounded perturbations.

Extends reducibility theory to non-integrable systems.

Addresses perturbations of order up to 1/2 on Zoll manifolds.

Abstract

In this article we prove a reducibility result for the linear Schr\"odinger equation on a Zoll manifold with quasi-periodic in time pseudo-differential perturbation of order less or equal than $1/2$. As far as we know, this is the first reducibility results for an unbounded perturbation of a linear system which is not integrable.