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

Alexander Arbieto·Jairo Bochi
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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.

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Alexander Arbieto, Jairo Bochi. 2002-11-01. $L^p$-generic cocycles have one-point Lyapunov spectrum. https://doi.org/10.1142/s0219493703000619

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