Discontinuity of Lyapunov exponents near fiber bunched cocycles

DOI10.1017/etds.2016.56zbMath1388.37064arXiv1509.04122OpenAlexW2264833532MaRDI QIDQ4643253

Clark Butler

Publication date: 24 May 2018

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

Full work available at URL: https://arxiv.org/abs/1509.04122

zbMATH Keywords

Bernoulli shiftLyapunov exponent\(\text{SL}(2,\mathbb{R})\)-cocycle

Mathematics Subject Classification ID

Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) General theory of random and stochastic dynamical systems (37H05)

Related Items (8)

Measurable rigidity of the cohomological equation for linear cocycles over hyperbolic systems ⋮ Lyapunov spectrum properties and continuity of the lower joint spectral radius ⋮ Continuity of Lyapunov exponents is equivalent to continuity of Oseledets subspaces ⋮ An invitation to \(SL_2(\mathbb{R})\) cocycles over random dynamics ⋮ Continuity of Lyapunov exponents in the \(C^0\) topology ⋮ Continuity of Lyapunov exponents for non-uniformly fiber-bunched cocycles ⋮ Continuity of Lyapunov exponents for cocycles with invariant holonomies ⋮ (Dis)continuity of Lyapunov exponents

Cites Work

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• Sharp error terms for return time statistics under mixing conditions
• Continuity of Lyapunov exponents for cocycles with invariant holonomies
• Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
• Genericity of zero Lyapunov exponents
• Continuity of Lyapunov exponents for random two-dimensional matrices
• Lectures on Lyapunov Exponents

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