薛定谔cocycle的动力学及谱行为研究

拟周期薛定谔cocycle来源于拟周期薛定谔算子的研究。而拟周期薛定谔算子是准晶和整数量子霍尔效应等物理问题的数学模型。拟周期薛定谔cocycle是一类典型且重要的动力系统，它存在非常丰富而重要的动力学及谱现象，因而吸引了许多一流数学家。本项目主要研究拟周期薛定谔cocycle的动力学及谱行为，例如Lyapunov指数及积分态密度的光滑性，cocycle的增长性，绝对连续谱特征函数的分层结构。

Quasiperiodic Schrodinger cocycle comes from the study of quasiperiodic Schrodinger operator, and quasi-periodic Schrodinger operator has strong backgrounds in quasicrystal and quantum Hall effect. Quasiperiodic Schrodinger cocycle is a typical and important subject in dynamical system, which displays rich and important dynamical and spectral behavior, thus it attracted many first-class mathematicians. This project will study the dynamical and spectral behavior of quasiperiodic Schrodinger cocycle, for example, the regularity of Lyapunov exponent and IDS, growth of cocycles, hierarchical structure of quasi-periodic eigenfunctions which support the absolutely continuous spectrum.