$L^p$-generic cocycles have one-point Lyapunov spectrum

Abstract

We show the sum of the first $k$ Lyapunov exponents of linear cocycles is an upper semicontinuous function in the $L^p$ topologies, for any $1\le p\le \infty$ and $k$. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the $L^p$-generic cocycle, $p<\infty$, are all equal.

8 pages. A gap in the previous version was corrected

References in corpus (2)

• Genericity of zero Lyapunov exponents
• The Lyapunov exponents of generic volume preserving and symplectic systems

Cited by in corpus (6)

• Continuity of Lyapunov Exponents for Random 2D Matrices
• Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for SL(2,R) cocycles
• Positive Lyapunov exponents for symplectic cocycles
• Simplicity over singular hyperbolicity
• Fine properties of Lp-cocycles which allow abundance of simple and trivial spectrum
• Trivial and simple spectrum for SL(2,R) cocycles with free base and fiber dynamics