Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications
Dynamical Systems
2021-01-28 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
For quasiperiodic Schr\"odinger operators with one-frequency analytic potentials, from dynamical systems side, it has been proved that the corresponding quasiperiodic Schr\"odinger cocycle is either rotations reducible or has positive Lyapunov exponent for all irrational frequency and almost every energy. From spectral theory side, the "Schr\"odinger conjecture" and the "Last's intersection spectrum conjecture" have been verified. The proofs of above results crucially depend on the analyticity of the potentials. People are curious about if the analyticity is essential for those problems, see open problems by Fayad-Krikorian and Jitomirskaya-Mar. In this paper, we prove the above mentioned results for ultra-differentiable potentials.
Keywords
Cite
@article{arxiv.2101.11150,
title = {Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications},
author = {Hongyu Cheng and Lingrui Ge and Jiangong You and Qi Zhou},
journal= {arXiv preprint arXiv:2101.11150},
year = {2021}
}