A new proof of continuity of Lyapunov exponents for a class of \( C^2 \) quasiperiodic Schrödinger cocycles without LDT

DOI10.3934/DCDS.2019121zbMath1408.37014OpenAlexW2908875528MaRDI QIDQ1735367

Jiahao Xu, Lin Lin Fu

Publication date: 28 March 2019

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2019121

zbMATH Keywords

Lyapunov exponentlarge deviation theoremSchrödinger cocycleDiophantine frequency

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) General theory of random and stochastic dynamical systems (37H05)

Related Items (2)

Hölder continuity of Lyapunov exponent for a family of smooth Schrödinger cocycles ⋮ New proof of continuity of Lyapunov exponents for a class of smooth Schrödinger cocycles with weak Liouville frequencies

Cites Work

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• Examples of discontinuity of Lyapunov exponent in smooth quasiperiodic cocycles
• Localization for a class of one dimensional quasi-periodic Schrödinger operators
• Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients
• On the multiplicative ergodic theorem for uniquely ergodic systems
• Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
• Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
• The dynamics of a class of quasi-periodic Schrödinger cocycles
• Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles
• Uniform positivity of Lyapunov exponent for a class of smooth Schrödinger cocycles with weak Liouville frequencies
• The Ten Martini problem
• Singular density of states measure for subshift and quasi-periodic Schrödinger operators
• Positive lyapunov exponents for quasiperiodic Szegő cocycles
• Density of positive Lyapunov exponents for 𝑆𝐿(2,ℝ)-cocycles
• Lyapunov exponents for some quasi-periodic cocycles
• Cantor Spectrum for a Class of $C^2$ Quasiperiodic Schrödinger Operators
• Genericity of zero Lyapunov exponents
• On nonperturbative localization with quasi-periodic potential.
• Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions

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