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 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.

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Cited by in corpus (5)

• Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation
• Reducibility of 1-D Quantum Harmonic Oscillator with Decaying Conditions on the Derivative of Perturbation Potentials
• 1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms
• Reducibility of 1-D quantum harmonic oscillator with new unbounded oscillatory perturbations
• Reducibility of relativistic Schrödinger equation with unbounded perturbations