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

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

2002-10-11

arxiv.org/abs/math/0210178v2

Stochastics and Dynamics, 3 (2003), 73-81. Corrigendum. Stochastics and Dynamics, 3 (2003), 419-420

Mathematics

Dynamical Systems

8 pages. A gap in the previous version was corrected

Scientific paper

10.1142/S0219493703000619

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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