Abstract:

We studied the Hlder continuity of the Lyapunov exponent associated with 1D quasiperiodic Jacobi operators(H_x,ω)(n)=-b(x+(n+1)ω)(n+1)-b(x+nω)(n-1)+a(x+nω)(n),n∈Zwhere x∈T, a(x),b(x) are real analytic on T and b(x) is not identically zero. Using the control theory of the Fourier coefficient of subharmonic function and the number property of ω, 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.

Key words: Jacobi operator, Lyapunov exponent, Holder continuous