Analyticity of the Lyapunov exponent of meromorphic monotonic cocycles

Abstract

In ¥cite , the authors considered analytic monotonic cocycles, and showed that the Lyapunov exponent of an analytic family of analytic monotonic cocycles is analytic. We extend the result of ¥cite , and show that a analytic family of meromorphic monotonic cocycles have analytic Lyapunov exponent. We then consider the quasiperiodic Schr¥“odinger operators that have meromorphic monotone potentials. Since the associated Schr¥“odinger cocycles are meromorphic and monotonic, by applying the result we show that the Lyapunov exponent of the associated Schr¥“odinger cocycle is analytic. For the proof we rely heavily on the techniques in ¥cite .