Density of positive Lyapunov exponents for 𝑆𝐿(2,ℝ)-cocycles

Avila, Artur

doi:10.1090/S0894-0347-2011-00702-9

Density of positive Lyapunov exponents for $\mathrm {SL}(2,\mathbb {R})$-cocycles
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by Artur Avila

J. Amer. Math. Soc. 24 (2011), 999-1014

DOI: https://doi.org/10.1090/S0894-0347-2011-00702-9

Published electronically: April 8, 2011

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Abstract:

We show that $\mathrm {SL}(2,\mathbb {R})$-cocycles with a positive Lyapunov exponent are dense in all regularity classes and for all non-periodic dynamical systems. For Schrödinger cocycles, we show prevalence of potentials for which the Lyapunov exponent is positive for a dense set of energies.

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