Reducibility, Lyapunov exponent, pure point spectra property for quasi-periodic wave operator

TL;DR

This paper proves the reducibility of a quasi-periodic wave operator with finite smooth potential, demonstrating it has pure point spectra and zero Lyapunov exponent, advancing understanding of spectral properties in quasi-periodic systems.

Contribution

It establishes reducibility and spectral properties of quasi-periodic wave operators with finite smooth potentials, which was previously not well understood.

Findings

Wave operator has pure point spectra

Lyapunov exponent is zero

Operator is reducible under certain conditions

Abstract

In the present paper, the reducibility is derived for linear wave equation of finite smooth and time-quasi-periodic potential subject to Dirichlet boundary condition. Moreover, it is proved that the corresponding wave operator possesses the property of pure point spectra and zero Lyapunov exponent.