Regularity and convergence rates for the Lyapunov exponents of linear cocycles

DOI10.3934/jmd.2013.7.619zbMath1321.37023arXiv1211.0648OpenAlexW2962753747MaRDI QIDQ2437970

Wilhelm Schlag

Publication date: 10 March 2014

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.0648

zbMATH Keywords

multiplicative ergodic theoremproducts of random matricesLyapunov exponents, shift dynamicsthe Avalanche Principle

Mathematics Subject Classification ID

Random matrices (algebraic aspects) (15B52) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (11)

Hölder regularity of the integrated density of states for quasi-periodic long-range operators on \(\ell^2(\mathbb{Z}^d)\) ⋮ Hölder continuity of Lyapunov exponent for a family of smooth Schrödinger cocycles ⋮ Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analytic multi-frequency quasi-periodic M(2,C) cocycles ⋮ Dynamics and spectral theory of quasi-periodic Schrödinger-type operators ⋮ Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles ⋮ Complex one-frequency cocycles ⋮ Effective multi-scale approach to the Schrödinger cocycle over a skew-shift base ⋮ The Avalanche principle and negative curvature ⋮ Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities ⋮ Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles ⋮ Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles

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