Uniform positivity of Lyapunov exponent for a class of smooth Schrödinger cocycles with weak Liouville frequencies

DOI10.1007/s11464-017-0619-2zbMath1377.37051OpenAlexW2589058672MaRDI QIDQ2358371

Jin Hao Liang, Po-Jen Kung

Publication date: 14 June 2017

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-017-0619-2

zbMATH Keywords

cocycleLyapunov exponentweak Liouville frequency

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (6)

Hölder continuity of Lyapunov exponent for a family of smooth Schrödinger cocycles ⋮ A new proof of continuity of Lyapunov exponents for a class of \( C^2 \) quasiperiodic Schrödinger cocycles without LDT ⋮ Joint continuity of Lyapunov exponent for finitely smooth quasi-periodic Schrödinger cocycles ⋮ Positive Lyapunov exponent for a class of quasi-periodic cocycles ⋮ Large coupling asymptotics for the Lyapunov exponent of finitely smooth quasi-periodic Schrödinger operators ⋮ New proof of continuity of Lyapunov exponents for a class of smooth Schrödinger cocycles with weak Liouville frequencies

Cites Work

• Examples of discontinuity of Lyapunov exponent in smooth quasiperiodic cocycles
• Localization for a class of one dimensional quasi-periodic Schrödinger operators
• The dynamics of the Hénon map
• 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
• Generic singular spectrum for ergodic Schrödinger operators
• Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential
• Discrete one-dimensional quasi-periodic Schrödinger operators with pure point spectrum
• Anderson localization for the discrete one-dimensional quasi-periodic Schrödinger operator with potential defined by a Gevrey-class function
• 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
• Method of variations of potential of quasi-periodic Schrödinger equations
• Positive lyapunov exponents for quasiperiodic Szegő cocycles
• Lyapunov exponents for some quasi-periodic cocycles
• 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

This page was built for publication: Uniform positivity of Lyapunov exponent for a class of smooth Schrödinger cocycles with weak Liouville frequencies