Continuity of the Lyapunov exponents for quasiperiodic cocycles

DOI10.1007/s00220-014-2068-zzbMath1317.81098arXiv1305.7504OpenAlexW2074467994MaRDI QIDQ462886

Silvius Klein, Pedro Duarte

Publication date: 22 October 2014

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

Full work available at URL: https://arxiv.org/abs/1305.7504

zbMATH Keywords

continuityLyapunov spectrumLyapunov exponentBanach manifoldquasiperiodic cocyclereal analytic linear cocycle

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) General theory of random and stochastic dynamical systems (37H05)

Related Items (12)

Hölder regularity of the integrated density of states for quasi-periodic long-range operators on \(\ell^2(\mathbb{Z}^d)\) ⋮ Continuity results and estimates for the Lyapunov exponent of Brownian motion in stationary potential ⋮ The set of smooth quasi-periodic Schrödinger cocycles with positive Lyapunov exponent is not open ⋮ Hölder continuity of Lyapunov exponent for a family of smooth Schrödinger cocycles ⋮ Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analytic multi-frequency quasi-periodic M(2,C) cocycles ⋮ Dynamics and spectral theory of quasi-periodic Schrödinger-type operators ⋮ A note on the theorem of Johnson, Palmer and Sell ⋮ Complex one-frequency cocycles ⋮ Continuity of Lyapunov exponents for cocycles with invariant holonomies ⋮ The Avalanche principle and negative curvature ⋮ Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles ⋮ Anderson localization for one-frequency quasi-periodic block Jacobi operators

Cites Work

• Unnamed Item
• Unnamed Item
• Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles
• Complex one-frequency cocycles
• Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential
• Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
• Analytic quasi-perodic cocycles with singularities and the Lyapunov exponent of extended Harper's model
• Régularité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes et applications. (Regularity of the largest characteristic exponent of products of independent random matrices and applications)
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
• 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: Continuity of the Lyapunov exponents for quasiperiodic cocycles