非退化Gevrey势能下拟周期Jacobi算子Lyapunov指数的正性与连续性  

Positivity and Continuity of Lyapunov Exponent of Quasi-periodicJacobi Operator under Non-degenerate Gevrey Potential Energy

作　　者：胡苗苗 陶凯[1] HU Miaomiao;TAO Kai(College of Science,Hohai University,Nanjing 210098,China)

机构地区：[1]河海大学理学院,南京210098

出　　处：《吉林大学学报（理学版）》2022年第6期1317-1325,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金青年科学基金(批准号:12001162)。

摘　　要：使用解析逼近、次调和函数、Birkhoff遍历定理、大偏差定理和雪崩原理等方法,研究拟周期Jacobi算子模型所对应的Lyapunov指数的正则性问题,得到了在势能为非退化的Gevrey函数条件下,若频率是强Diophantine数,且势能的系数充分大时,Lyapunov指数的正性和连续性都成立的结果.从而将SL(2,ℝ)的Schr dinger斜积流结果推广到了GL(2,ℝ)的Jacobi斜积流上.We used the methods such as the analytical approximation,the subharmonic function,the Birkhoff ergodic theorem,the large deviation theorem and the avalanche principle to study the regularity of the Lyapunov exponent corresponding to the quasi-periodic Jacobi operator model.Under the condition that the potential energy is a non-degenerate Gevrey function,if the frequency is a strong Diophantine number and the coefficient of potential energy is large enough,we obtain the results that Lyapunov exponent is positive and continuous.Thus,the result of the Schr dinger cocycle in SL(2,ℝ)is extended to the Jacobi cocycle in GL(2,ℝ).

关 键 词：拟周期Jaocbi算子 非退化Gevrey函数 LYAPUNOV指数 连续性 正性 

分 类 号：O193[理学—数学]