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We prove the Holder continuity of the Lyapunov exponent for quasi-periodic Schrodinger cocycles with a $C^2$ cos-type potential and any fixed Liouvillean frequency, provided the coupling constant is sufficiently large. Moreover, the Holder exponent is independent of the frequency and the coupling constant.
We construct discontinuous point of the Lyapunov exponent of quasiperiodic Schrodinger cocycles in the Gevrey space $G^{s}$ with $s>2$. In contrast, the Lyapunov exponent has been proved to be continuous in the Gevrey space $G^{s}$ with $s<2$ cite{kl
Let $G$ be a semisimple Lie group acting on a space $X$, let $mu$ be a compactly supported measure on $G$, and let $A$ be a strongly irreducible linear cocycle over the action of $G$. We then have a random walk on $X$, and let $T$ be the associated s
We prove that generic fiber-bunched and Holder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a u-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched cocycles.
We prove that in an open and dense set, Symplectic linear cocycles over time one maps of Anosov flows, have positive Lyapunov exponents for SRB measures.
Criteria for the simplicity of the Lyapunov spectra of linear cocycles have been found by Furstenberg, Guivarch-Raugi, Goldsheid-Margulis and, more recently, Bonatti-Viana and Avila-Viana. In all the cases, the authors consider cocycles over hyperbol