Abstract: By using the methods including Weyl’s difference principle, large deviation theorem, avalanche principle and so on, we considered the problem of the Lyapunov exponent positivity and continuity of the discrete analytic Schrdinger operator defined by the high order skew shift T_ω. We proved that if the potential energy factor was big enough, then the Lyapunov exponent of the system was positive and week Hlder continuity. This results extended the conclusion about the Lyapunov exponent positivity and continuity with the lower order skew shift to the one with the high order skew shift.

Key words: Schrodinger operator, Lyapunov exponent, high order skew shift