弱Liouville频率下解析拟周期Jacobi算子Lyapunov指数的Hölder连续性

Hölder Continuity of Lyapunov Exponent for Analytic Quasi-periodic Jacobi Operators with Weak Liouville Frequency

考虑一维拟周期Jacobi算子(Hx,ωΦ)(n)=-b(x+(n+1)ω)Φ(n+1)-b(x+nω)Φ(n-1)+a(x+nω)Φ(n),n∈Z Lyapunov指数的连续性,其中:x∈T;a(x),b(x)在T上实解析且b(x)不恒为零.运用次调和函数的Fourier系数控制理论,结合ω的数论性质,通过分析得到Jacobi算子的大偏差定理及该算子在弱Liouville频率下其Lyapunov指数的Hlder连续性.

We studied the Hlder continuity of the Lyapunov exponent associated with 1-D quasiperiodic Jacobi operators（Hx,ωΦ）（n）=-b（x＋（n＋1）ω）Φ（n＋1）-b（x＋nω）Φ（n-1）＋a（x＋nω）Φ（n）, n∈Z,where x∈T,a（x）,b（x）are real analytic onTTand b（x）is not identically zero.Using the control theory of the Fourier coefficient of subharmonic function and the number property ofω,we obtained the large deviation theorem through more detailed analysis and the Hlder continuity of the Lyapunov exponent for the operators with weak Liouville frequency by further using the avalanche principle.