New proof of continuity of Lyapunov exponents for a class of smooth Schrödinger cocycles with weak Liouville frequencies

We reconsider the continuity of the Lyapunov exponents for a class of smooth Schrödinger cocycles with a C2 cos-type potential and a weak Liouville frequency.We propose a new method to prove that the Lyapunov exponent is continuous in energies.In particular,a large deviation theorem is not needed in the proof.