Nonexistence of Lyapunov Exponents for Matrix Cocycles

Abstract

It follows from Oseledec Multiplicative Ergodic Theorem that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In strong contrast, for any dynamical system $f:X\to X$ with exponential specification property and a H$\ddot{\text{o}}$lder continuous matrix cocycle $A:X\to G(m,\mathbb{R})$, we show here that if there exist ergodic measures with different Lyapunov spectrum, then the Lyapunov-irregular set of $A$ is residual (i.e., containing a dense $G_{\delta }$ set).

arXiv admin note: substantial text overlap with arXiv:0808.0350 by other authors

References in corpus (1)

• Lyapunov `Non-typical' Points of Matrix Cocycles and Topological Entropy

Cited by in corpus (3)

• Lyapunov exponents for random maps
• Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points
• A remark on the invertibility of semi-invertible cocycles