Positive Lyapunov exponents for a dense set of bounded measurable SL(2, ℝ)-cocycles

DOI10.1017/S0143385700006775zbMath0759.58025MaRDI QIDQ4024957

Oliver Knill

Publication date: 18 February 1993

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

zbMATH Keywords

Lyapunov exponentsmatrix cocyclescircle-valued cocycles

Mathematics Subject Classification ID

Ergodic theory (37A99)

Related Items (15)

Dynamics of generic 2-dimensional linear differential systems ⋮ Lyapunov exponents for linear homogeneous differential equations ⋮ The density of linear symplectic cocycles with simple Lyapunov spectrum in \({\mathcal G}_{IC}(X, \mathrm{SL}(2,\mathbb R))\) ⋮ Continuity of Lyapunov exponents for random two-dimensional matrices ⋮ Extremal exponents of random products of conservative diffeomorphisms ⋮ Fine properties of \(L^p\)-cocycles which allow abundance of simple and trivial spectrum ⋮ On \({SL(2, \mathbb R)}\) valued smooth proximal cocycles and cocycles with positive Lyapunov exponents over irrational rotation flows ⋮ Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles ⋮ Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases ⋮ Lyapunov exponents for random perturbations of some area-preserving maps including the standard map ⋮ Stability of equilibrium asset pricing models: a necessary and sufficient condition ⋮ (Dis)continuity of Lyapunov exponents ⋮ Moduli of continuity for the Lyapunov exponents of random 𝐺𝐿(2)-cocycles ⋮ Topological classification of linear hyperbolic cocycles ⋮ A formula with some applications to the theory of Lyapunov exponents

Cites Work

• A proof of Oseledec's multiplicative ergodic theorem
• 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
• Principles for the design of billiards with nonvanishing Lyapunov exponents
• On circle-valued cocycles of an ergodic measure preserving transformation
• Ergodic theory of differentiable dynamical systems
• Analycity properties of the characteristic exponents of random matrix products
• Cohomology of step functions under irrational rotations
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Noncommuting Random Products

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