高阶斜积映射下Schr?dinger算子的Lyapunov指数

Lyapunov Exponent of Schr?dinger Operator with High Order Skew Shift

利用Weyl差分原理、大偏差定理和雪崩原理等方法,考虑高阶斜积映射T_ω定义下离散解析Schr?dinger算子的Lyapunov指数正性和连续性问题.证明了当其势能系数充分大时,系统的Lyapunov指数关于能量参数E是弱H?lder连续的,且是正的.从而将低阶斜积映射下的Lyapunov指数连续性和正性的结论推广到了高阶情形.

By using the methods including Weyl＇s difference principle, large deviation theorem, avalanche principle and so on, we considered the problem of the Lyapunov exponent positivity and continuity of the discrete analytic Schrodinger operator defined by the high order skew shift Tw. We proved that if the potential energy factor was big enough, then the Lyapunov exponent of the system was positive and week Holder continuity. This results extended the conclusion about the Lyapunov exponent positivity and continuity with the lower order skew shift to the one with the high order skew shift.