拟周期Gevrey势能下Jacobi算子的Lyapunov指数的全域连续性  

Global continuity of the Lyapunov exponent of Quasi-periodic Jacobio perator with Gevrey potential

作　　者：杨妍 陶凯[1] YANG Yan;TAO Kai(College of Science,Hohai University,Nanjing 210098,China)

机构地区：[1]河海大学理学院,江苏南京210098

出　　处：《湖北大学学报（自然科学版）》2023年第3期305-311,共7页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金青年项目(12001162)资助。

摘　　要：Lyapunov指数一直是动力系统中的核心概念与研究热点.本文中研究拟周期Jacobi算子模型所对应的Lyapunov指数.我们使用解析逼近,次调和函数,Birkhoff遍历定理,大偏差定理和雪崩原理等方法和理论,证明在势能为s-Gevrey函数(s<2)的条件下,若频率是强Diophantine数,Lyapunov指数关于能量是全域连续的.The Lyapunov exponent is a core conception and a hot research topic in the dynamical systems.In this paper,we considered the discrete quasi-periodic Jacobi operators with Gevrey potential.We applied the methods such as analytical approximation,the subharmonic function theory,the Birkhoff ergodic theorem,the large deviation theorem,and the avalanche principle to prove that for the s-Gevrey potential(s<2)with the strong Diophantine frequency,the Lyapunov exponent was global continuity in E.

关 键 词：拟周期Jacobi算子 Gevrey函数 LYAPUNOV指数 全域连续性 

分 类 号：O193[理学—数学]