Complex one-frequency cocycles
By Artur Avila, S. Jitomirskaya, Christian Sadel. 2013
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We show that on a dense open set of analytic one-frequency complex valued cocycles in arbitrary dimension Oseledets filtration is either dominated or trivial. The underlying mechanism is different from that of the Bochi-Viana Theorem for continuous cocycles, which links non-domination with discontinuity of the Lyapunov exponent. Indeed, in our setting the Lyapunov exponents are shown to depend continuously on the cocycle, even if the initial irrational frequency is allowed to vary. On the other hand, this last property provides a good control of the periodic approximations of a cocycle, allowing us to show that domination can be characterized, in the presence of a gap in the Lyapunov spectrum, by additional regularity of the dependence of sums of Lyapunov exponents.
Subfields: Computer Networks and Communications, Spectroscopy, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/7db6807ea51bd498d90589a73352159c93a464d7
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In Computer Networks and Communications
In Spectroscopy
In Statistical and Nonlinear Physics
Citations in the corpus
- Uniform Positivity and Continuity of Lyapunov Exponents for a Class of $C^2$ Quasiperiodic Schrödinger Cocycles (2013, methodology): “al M(2,C) case in [JiMar2]. More recently, a completely different proof, not using LDT or Avalanche principle, and extending to the general M(d,C), d≥ 2, case was developed in Avila-Jitomirskaya-Sadel [AvJiSa]. All these results however rely heavily on analyticity of the cocycle map. Thus, Theorem 2 ”