线性斜积流的Lyapunov指数的连续性研究

cocycle的Lyapunov指数的连续性问题作为动力系统研究热点离散Schrödinger算子问题的一个重要延伸，在最近几年收到不少数学家的关注。本项目研究在d维解析拟周期cocycle的条件下，当部分Lyapunov指数相等时，此d个Lyapunov指数是否连续；同时，申请人也想证明在2维解析拟周期cocycle的条件下，其Lyapunov指数是Hölder连续的，并且其Hölder指数不依赖于Lyapunov指数大小。

The continuity of the Lyapunov exponent for the cocycle is one important evolution of the discrete Schrödinger operator problem， which is a hot spot of Dynamic system, researched by several mathematicians in these years.This project will study whether the d Lyapunov exponents of d dimension analytic quasi-periodic cocycles are continue, when some of these Lyapunov exponents are equal; the applicant also want to prove that the Lyapunov exponents of two dimension analytic quasi-periodic cocycles are Hölder continue, and their Hölder exponents do not depend on the Lyapunov exponent.