DOI10.1023/A:1019751801035zbMath1039.81019arXivmath-ph/0110040OpenAlexW1484558217WikidataQ97672450 ScholiaQ97672450MaRDI QIDQ1397381
Jean Bourgain, Svetlana Ya. Jitomirskaya
Publication date: 6 August 2003
Published in: Journal of Statistical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0110040
Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators ⋮
Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications ⋮
Homogeneity of the spectrum for quasi-periodic Schrödinger operators ⋮
Hölder regularity of the integrated density of states for quasi-periodic long-range operators on \(\ell^2(\mathbb{Z}^d)\) ⋮
Lyapunov Exponents, Sensitivity, and Stability for Non-Autonomous Discrete Systems ⋮
Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles ⋮
Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮
What are Lyapunov exponents, and why are they interesting? ⋮
Continuity results and estimates for the Lyapunov exponent of Brownian motion in stationary potential ⋮
The Ten Martini problem ⋮
Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs ⋮
Large deviation theorems for Dirichlet determinants of analytic quasi-periodic Jacobi operators with Brjuno-Rüssmann frequency ⋮
The set of smooth quasi-periodic Schrödinger cocycles with positive Lyapunov exponent is not open ⋮
Sharp \(\frac{1}{2}\)-Hölder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrödinger cocycles ⋮
Examples of discontinuity of Lyapunov exponent in smooth quasiperiodic cocycles ⋮
On the Lyapunov exponent of certain \(SL (2,\mathbb R)\)-valued cocycles. II ⋮
Limit-periodic Schrödinger operators with a discontinuous Lyapunov exponent ⋮
Continuity of the measure of the spectrum for quasiperiodic Schrödinger operators with rough potentials ⋮
Monotonic cocycles ⋮
Analytic quasi-periodic Schrödinger operators and rational frequency approximants ⋮
Arithmetic phase transitions for mosaic Maryland model ⋮
Universal supercritical behavior for some skew-product maps ⋮
Ballistic transport for limit-periodic Schrödinger operators in one dimension ⋮
Non-perturbative positivity and weak Hölder continuity of Lyapunov exponent for some discrete multivariable Jacobi operators ⋮
On the Lyapunov exponent for some quasi-periodic cocycles with large parameter ⋮
Ballistic Transport for One‐Dimensional Quasiperiodic Schrödinger Operators ⋮
Global theory of one-frequency Schrödinger operators ⋮
Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators ⋮
Upper bounds on quantum dynamics in arbitrary dimension ⋮
Stability of the non-critical spectral properties i: arithmetic absolute continuity of the integrated density of states ⋮
Hölder continuity of Lyapunov exponent for a family of smooth Schrödinger cocycles ⋮
Anosov-Katok constructions for quasi-periodic \(\operatorname{SL}(2, \mathbb{R})\) cocycles ⋮
Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analytic multi-frequency quasi-periodic M(2,C) cocycles ⋮
Exact mobility edges for 1D quasiperiodic models ⋮
Schrödinger operators with dynamically defined potentials ⋮
Dynamics and spectral theory of quasi-periodic Schrödinger-type operators ⋮
Some remarks on the dynamics of the almost Mathieu equation at critical coupling* ⋮
On \(SL(2,\mathbb{R})\)-cocycles over irrational rotations with secondary collisions ⋮
An estimate on the number of eigenvalues of a quasiperiodic Jacobi matrix of size \(n\) contained in an interval of size \(n^{-C}\) ⋮
Large coupling asymptotics for the entropy of quasi-periodic operators ⋮
One-dimensional quasiperiodic operators: global theory, duality, and sharp analysis of small denominators ⋮
Continuity of Lyapunov exponents for random two-dimensional matrices ⋮
A spectral alternative for continuous families of self-adjoint operators ⋮
On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations ⋮
Continuity of the Lyapunov exponent for analytic quasi-periodic cocycles with singularities ⋮
Uniform convergence of Schrödinger cocycles over bounded Toeplitz subshift ⋮
OLD AND NEW RESULTS ON STRANGE NONCHAOTIC ATTRACTORS ⋮
Continuity of the Lyapunov exponents for quasiperiodic cocycles ⋮
Complex one-frequency cocycles ⋮
All couplings localization for quasiperiodic operators with monotone potentials ⋮
A new proof of continuity of Lyapunov exponents for a class of \( C^2 \) quasiperiodic Schrödinger cocycles without LDT ⋮
Universal hierarchical structure of quasiperiodic eigenfunctions ⋮
Second phase transition line ⋮
Ergodic Schrödinger operators in the infinite measure setting ⋮
Spectral characteristics of the unitary critical almost-Mathieu operator ⋮
A lower bound on the Lyapunov exponent for the generalized Harper's model ⋮
Continuity of Lyapunov exponent for analytic quasi-periodic cocycles on higher-dimensional torus ⋮
Analytic quasi-perodic cocycles with singularities and the Lyapunov exponent of extended Harper's model ⋮
Probabilistic averages of Jacobi operators ⋮
Ergodic Jacobi matrices and conformal maps ⋮
Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles ⋮
Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling ⋮
A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem ⋮
Some connections between almost periodic and periodic discrete Schrödinger operators with analytic potentials ⋮
The exponential decay of eigenfunctions for tight-binding Hamiltonians via landscape and dual landscape functions ⋮
Continuity of Lyapunov exponents for cocycles with invariant holonomies ⋮
Mixed spectral types for the one-frequency discrete quasi-periodic Schrödinger operator ⋮
Lyapunov exponents of discrete quasi-periodic Gevrey Schrödinger equations ⋮
Combinatorial rigidity for unicritical polynomials ⋮
Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle ⋮
Uniform hyperbolicity and its relation with spectral analysis of 1D discrete Schrödinger operators ⋮
Joint continuity of Lyapunov exponent for finitely smooth quasi-periodic Schrödinger cocycles ⋮
(Dis)continuity of Lyapunov exponents ⋮
Transport exponents of states with large support ⋮
Unnamed Item ⋮
The Avalanche principle and negative curvature ⋮
On singularly perturbed linear cocycles over irrational rotations ⋮
Continuity of the Lyapunov exponent for analytic quasiperiodic cocycles ⋮
Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles ⋮
Singular analytic linear cocycles with negative infinite Lyapunov exponents ⋮
Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications ⋮
H\"older continuity of Lyapunov exponent for quasi-periodic Jacobi operators ⋮
Lyapunov exponents of linear cocycles over Markov shifts ⋮
Lyapunov exponents for discrete, quasi-periodic Schrödinger operators ⋮
Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles ⋮
Arithmetic Spectral Transitions for the Maryland Model ⋮
Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential
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