Positive Lyapunov exponents for a class of deterministic potentials

DOI10.1007/BF02101838zbMath0821.60070OpenAlexW2079200362MaRDI QIDQ1894840

Thomas Spencer, Victor Chulaevskij

Publication date: 22 August 1995

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02101838

zbMATH Keywords

Schrödinger operatorsymbolic dynamicsergodic potentialLyapunov exponent of Schrödinger operators

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44)

Related Items (17)

Positive Lyapunov exponent for some Schrödinger cocycles over multidimensional strongly expanding torus endomorphisms ⋮ Positive Lyapunov exponents for a class of ergodic orthogonal polynomials on the unit circle ⋮ The almost sure essential spectrum of the doubling map model is connected ⋮ Localization for random operators with non-monotone potentials with exponentially decaying correlations ⋮ Clock statistics for 1d Schrödinger operators ⋮ Schrödinger operators with potentials generated by hyperbolic transformations. I: Positivity of the Lyapunov exponent ⋮ The Schwartzman group of an affine transformation ⋮ Positive Lyapunov exponent for some Schrödinger cocycles over strongly expanding circle endomorphisms ⋮ Parametric Furstenberg theorem on random products of \(\mathrm{SL}(2, \mathbb{R})\) matrices ⋮ Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle ⋮ Almost everywhere positivity of the Lyapunov exponent for the doubling map ⋮ Hölder continuity of the Lyapunov exponents of linear cocycles over hyperbolic maps ⋮ Multiscale analysis for ergodic Schrödinger operators and positivity of Lyapunov exponents ⋮ Spectral type of a class of random Jacobi operators ⋮ Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles ⋮ A note on Lyapunov exponents of deterministic strongly mixing potentials ⋮ On the Lyapunov exponents for a class of circle diffeomorphisms driven by expanding circle endomorphisms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kotani theory for one dimensional stochastic Jacobi matrices
• Anomalies in the one-dimensional Anderson model at weak disorder
• Support theorems for random Schrödinger operators
• Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications
• On Products of Random Matrices and Operators
• Noncommuting Random Products

This page was built for publication: Positive Lyapunov exponents for a class of deterministic potentials