高维解析Jacobi算子的Lyapunov指数的log-Hölder连续性

The log-Hölder continuity of the Lyapunov exponent of high dimension alanalytic Jacobi operator

Lyapunov指数是动力系统中的核心概念,一直是本领域内的热门和难点问题.本研究解析Jacobi算子对应的Lyapunov指数关于能量的连续性问题.我们使用次调和函数理论,Birkhoff遍历定理,大偏差定理和雪崩原理等方法,解决了高维解析Jacobi算子的这一问题.具体地,我们证明了,如果算子对应的Lyapunov指数在某一点是正的,则Lyapunov指数在这一点处是log-Hölder连续的.

The Lyapunov exponent is the core concept in the dynamical systems,and which has always been a hot and difficult problem in this field.The purpose of this paper is to study the continuity of Lyapunov exponents of the Jacobi operators with analytic functions on high dimension torus.We used the methods such as the subharmonic function theory,the Birkhoff ergodic theorem,the large deviation theorem,and the avalanche principle to solve this problem.Specifically,we proved that if the Lyapunov exponent was positive at a certain point,the Lyapunov exponent was log-Hölder continuous at this point.