KAM Theorem for a Hamiltonian system with Sublinear Growth Frequencies at Infinity

TL;DR

This paper establishes an infinite-dimensional KAM theorem for Hamiltonian systems with sublinear frequency growth at infinity, and applies it to prove the reducibility of a quasi-periodically forced linear fractional Schrödinger equation.

Contribution

It introduces a KAM theorem tailored for systems with sublinear frequency growth and demonstrates its application to a specific PDE, expanding the scope of reducibility results.

Findings

Proved an infinite-dimensional KAM theorem for sublinear frequencies.

Established reducibility of the fractional Schrödinger equation with quasi-periodic forcing.

Extended KAM theory applicability to new classes of Hamiltonian systems.

Abstract

We prove an infinite-dimensional KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity. As an application, we prove the reducibility of the linear fractional Schr\"odinger equation with quasi-periodic time-dependent forcing.