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

Alexander Arbieto; Jairo Bochi

doi:10.1142/S0219493703000619

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

Dynamical Systems 2009-12-18 v2

Authors: 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.

Keywords

lyapunov exponents lp spaces and inequalities

Cite

@article{arxiv.math/0210178,
  title  = {$L^p$-generic cocycles have one-point Lyapunov spectrum},
  author = {Alexander Arbieto and Jairo Bochi},
  journal= {arXiv preprint arXiv:math/0210178},
  year   = {2009}
}

Comments

8 pages. A gap in the previous version was corrected

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