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

Jairo Bochi | Arbieto, Alexander

Keywords: Lyapunov Exponents | linear cocyles

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.

Anexos:

• l1generic.pdf