Continuity of Lyapunov Exponents for Random 2D Matrices

Abstract

The Lyapunov exponents of locally constant GL(2;C)-cocycles over Bernoulli shifts depend continuously on the cocycle and on the invariant probability. The Oseledets decomposition also depends continuously on the cocycle, in measure.

References in corpus (3)

• Genericity of zero Lyapunov exponents
• Lusin's Theorem and Bochner Integration
• $L^p$-generic cocycles have one-point Lyapunov spectrum

Cited by in corpus (10)

• Lyapunov exponents for random perturbations of some area-preserving maps including the standard map
• Continuity of the Lyapunov exponents for quasiperiodic cocycles
• Discontinuity of Lyapunov Exponents Near Fiber Bunched Cocycles
• Quasi-Periodic Schrödinger Cocycles with Positive Lyapunov Exponent are not Open in the Smooth Topology
• Continuity of the Oseledets Decomposition
• Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles
• Continuity of Lyapunov exponents for non-uniformly fiber-bunched cocycles
• A Note on the Continuity of Oseledets Subspaces for Fiber-Bunched Cocycles
• Some Spectrum Property of Periodic Coupling AMO Operator
• Hilbert Space Lyapunov Exponent stability