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

Abstract

We reconsider the continuity of the Lyapunov exponents for a class of smooth Schrödinger cocycles with a C^2 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.

Key words： Schrödinger cocycle; Lyapunov exponent (LE); weak Liouville frequency; C^2 cos-type potential; large deviation theorem (LDT)

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