Geodesic
Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
Marcelo Viana1
1 IMPA <br/>22460-320 Rio de Janeiro<br/> Brazil
Annals of mathematics, Tome 167 (2008) no. 2, pp. 643-680.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that for any $s>0$ the majority of $C^s$ linear cocycles over any hyperbolic (uniformly or not) ergodic transformation exhibit some nonzero Lyapunov exponent: this is true for an open dense subset of cocycles and, actually, vanishing Lyapunov exponents correspond to codimension-$\infty$. This open dense subset is described in terms of a geometric condition involving the behavior of the cocycle over certain heteroclinic orbits of the transformation.
DOI : 10.4007/annals.2008.167.643

Marcelo Viana 1

1 IMPA <br/>22460-320 Rio de Janeiro<br/> Brazil 
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Marcelo Viana. Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. Annals of mathematics, Tome 167 (2008) no. 2, pp. 643-680. doi : 10.4007/annals.2008.167.643. http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.167.643/

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