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The dynamics of a class of quasi-periodic Schrödinger cocycles (Q2339211)

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English	The dynamics of a class of quasi-periodic Schrödinger cocycles	scientific article

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scholarly article

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The dynamics of a class of quasi-periodic Schrödinger cocycles (English)

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Kristian Bjerklöv

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Annales Henri Poincaré

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publication date

31 March 2015

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full work available at URL

https://arxiv.org/abs/1311.5394

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zbMATH Keywords

quasiperiodic Schrödinger cocycle

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Morse function

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Lyapunov exponent

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eigenfunctions

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MaRDI profile type

MaRDI publication profile

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Density of positive Lyapunov exponents for 𝑆𝐿(2,ℝ)-cocycles

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On iterations of \(1-\alpha x^2\) on \((-1,1)\)

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Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrödinger equations

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Dynamics of the quasi-periodic Schrödinger cocycle at the lowest energy in the spectrum

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Positive Lyapunov exponent and minimality for the continuous 1-d quasi-periodic Schrödinger equation with two basic frequencies

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Explicit examples of arbitrarily large analytic ergodic potentials with zero Lyapunov exponent

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Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations

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Universal asymptotics in hyperbolicity breakdown

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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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On nonperturbative localization with quasi-periodic potential.

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Method of variations of potential of quasi-periodic Schrödinger equations

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On the abundance of aperiodic behaviour for maps on the interval

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Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension

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The rotation number for finite difference operators and its properties

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Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

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Discrete one-dimensional quasi-periodic Schrödinger operators with pure point spectrum

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Localization for a class of one dimensional quasi-periodic Schrödinger operators

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Noncommuting Random Products

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Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions

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Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues

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On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations

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Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2

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Absolutely continuous invariant measures for one-parameter families of one-dimensional maps

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Metal-insulator transition for the almost Mathieu operator

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The rotation number for almost periodic potentials

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Ergodic theory and linear differential equations

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The recurrent Hill's equation

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Strange non-chaotic attractors in quasiperiodically forced circle maps

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Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients

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OLD AND NEW RESULTS ON STRANGE NONCHAOTIC ATTRACTORS

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Strange non-chaotic attractors in quasi-periodically forced circle maps: Diophantine forcing

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Anderson localization for the discrete one-dimensional quasi-periodic Schrödinger operator with potential defined by a Gevrey-class function

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Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators

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Cantor spectrum for the almost Mathieu operator

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A nonperturbative Eliasson's reducibility theorem

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Kotani theory for one dimensional stochastic Jacobi matrices

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Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential

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Positive Lyapunov exponents for Schrödinger operators with quasi- periodic potentials

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Difference almost-periodic Schrödinger operators: Corollaries of localization

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Examples of discontinuity of Lyapunov exponent in smooth quasiperiodic cocycles

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Lyapunov exponents for some quasi-periodic cocycles

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Identifiers

zbMATH Open document ID

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10.1007/s00023-014-0330-8

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2339211

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