Uniform gap in Lyapunov exponents and dominated splitting for linear cocycles

Abstract

Given a linear cocycle over an ergodic homeomorphism on a compact metric space, we show that the existence of a uniform gap between the $p$-th and $(p+1)$-th Lyapunov exponent on a $C^0$-neighbourhood implies the existence of a dominated splitting of index $p$.

30 pages, 1 figure. Corrected some proofs. Tiny rewrite of introduction with more references

References in corpus (1)

• Genericity of zero Lyapunov exponents