Analyticity of the Lyapunov exponent of meromorphic monotonic cocycles. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Takahashi, Yuki
• Is Part Of: Dynamical systems. Volume 37:Issue 2(2022)
• Page Start: 328
• Page End: 332
• Publication Date: 2022-04-03
• Subjects: Quasiperiodic cocycle -- Lyapunov exponent; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2022.2049707
• Languages: English
• ISSNs: 1468-9367

Abstract

Abstract : In ¥cite { A K }, 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 { A K }, 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 { A K } .