Continuity of Lyapunov exponents for random two-dimensional matrices

DOI10.1017/etds.2015.116zbMath1379.37100OpenAlexW2335035713MaRDI QIDQ5364858

Carlos Bocker-Neto, Marcelo Viana

Publication date: 28 September 2017

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://www.cambridge.org/core/product/F859005F09EA69849D9313B967C0B4C6

zbMATH Keywords

Bernoulli shiftLyapunov exponentrandom two-dimensional matrix

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)

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Cites Work

• Lyapunov numbers for the almost periodic Schrödinger equation
• Random matrix products and measures on projective spaces
• The Lyapunov exponents of generic volume-preserving and symplectic maps
• Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential
• Extremal Lyapunov exponents: an invariance principle and applications
• Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model
• Analycity properties of the characteristic exponents of random matrix products
• Convex analysis and measurable multifunctions
• Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
• 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)
• Perturbations of random matrix products in a reducible case
• [https://portal.mardi4nfdi.de/wiki/Publication:3311395 Loi des grands nombres et perturbations pour des produits r�ductibles de matrices al�atoires ind�pendantes]
• Foundations of Ergodic Theory
• C¹-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents
• Perturbations of random matrix products
• Positive Lyapunov exponents for a dense set of bounded measurable SL(2, ℝ)-cocycles
• On the simplicity of the Lyapunov spectrum of products of random matrices
• Genericity of zero Lyapunov exponents
• L^p-GENERIC COCYCLES HAVE ONE-POINT LYAPUNOV SPECTRUM
• Lectures on Lyapunov Exponents
• Products of Random Matrices
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