Geodesic
Density of positive Lyapunov exponents for 𝑆𝐿(2,ℝ)-cocycles
Avila, Artur1, 2
1 Institut de Mathématiques de Jussieu, CNRS UMR 7586, 175 rue du Chevaleret, 75013, Paris, France
2 IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil
Journal of the American Mathematical Society, Tome 24 (2011) no. 4, pp. 999-1014

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-2011-00702-9

Avila, Artur 1, 2

1 Institut de Mathématiques de Jussieu, CNRS UMR 7586, 175 rue du Chevaleret, 75013, Paris, France
2 IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil 
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Avila, Artur. Density of positive Lyapunov exponents for 𝑆𝐿(2,ℝ)-cocycles. Journal of the American Mathematical Society, Tome 24 (2011) no. 4, pp. 999-1014. doi: 10.1090/S0894-0347-2011-00702-9

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