Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles
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Publication:2633093
DOI10.1007/s00209-018-2147-5zbMath1482.37031arXiv1706.08649OpenAlexW2963773364MaRDI QIDQ2633093
Claire Chavaudret, Qi Zhou, Jiangong You, Ao Cai
Publication date: 8 May 2019
Published in: Mathematische Zeitschrift (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.08649
Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)
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Cites Work
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- Embedding of analytic quasi-periodic cocycles into analytic quasi-periodic linear systems and its applications
- Examples of discontinuity of Lyapunov exponent in smooth quasiperiodic cocycles
- Complex one-frequency cocycles
- A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies
- Hölder continuity of the rotation number for quasi-periodic co-cycles in \({SL(2, \mathbb R)}\)
- Almost periodic Schrödinger operators. II: The integrated density of states
- Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential
- Almost localization and almost reducibility
- Monotonic cocycles
- Global theory of one-frequency Schrödinger operators
- Rigidity results for quasiperiodic \(\mathrm{SL}(2, \mathbb R)\)-cocycles
- Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues
- Analycity properties of the characteristic exponents of random matrix products
- The rotation number for almost periodic potentials
- Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
- On the multiplicative ergodic theorem for uniquely ergodic systems
- Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
- Hölder regularity of integrated density of states for the almost Mathieu operator in a perturbative regime
- Sharp phase transitions for the almost Mathieu operator
- All couplings localization for quasiperiodic operators with monotone potentials
- Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems
- Continuity of Lyapunov exponents for cocycles with invariant holonomies
- Localization for quasiperiodic Schrödinger operators with multivariable Gevrey potential functions
- Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles
- Forced vibrations of wave equations with non-monotone nonlinearities
- Almost reducibility for finitely differentiable SL(2,\mathbb{R}) -valued quasi-periodic cocycles
- Continuity of the Lyapunov exponent for analytic quasiperiodic cocycles
- Generalized implicit function theorems with applications to some small divisor problems, I
- Genericity of zero Lyapunov exponents
- Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles
- Continuity of Lyapunov exponents for random two-dimensional matrices
- Lectures on Lyapunov Exponents
- Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions
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