no. 3
A uniform dichotomy for generic SL (2,ℝ) cocycles over a minimal base
[Une dichotomie uniforme pour des cocycles à valeurs dans SL (2,ℝ) au-dessus d’une dynamique minimale]
Bulletin de la Société Mathématique de France, Tome 135 (2007) no. 3, pp. 407-417.

On considère des cocycles continus à valeurs dans SL (2,ℝ) au-dessus d’un homéomorphisme minimal d’un ensemble compact de dimension finie. On montre que le cocycle générique soit est uniformément hyperbolique, soit possède une croissance sous-exponentielle uniforme.

We consider continuous SL (2,ℝ)-cocycles over a minimal homeomorphism of a compact set K of finite dimension. We show that the generic cocycle either is uniformly hyperbolic or has uniform subexponential growth.

DOI : 10.24033/bsmf.2540
Classification : 37H15
Keywords: cocycle, minimal homeomorphism, uniform hyperbolicity, Lyapunov exponents
Mot clés : cocycle, homéomorphisme minimal, hyperbolicité uniforme, exposants de Liapounov 
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     title = {A uniform dichotomy for generic ${\rm SL}(2,{\mathbb {R}})$ cocycles over a minimal base},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {407--417},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {135},
     number = {3},
     year = {2007},
     doi = {10.24033/bsmf.2540},
     mrnumber = {2430187},
     zbl = {1217.37017},
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     url = {http://www.numdam.org/articles/10.24033/bsmf.2540/}
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Avila, Artur; Bochi, Jairo. A uniform dichotomy for generic ${\rm SL}(2,{\mathbb {R}})$ cocycles over a minimal base. Bulletin de la Société Mathématique de France, Tome 135 (2007) no. 3, pp. 407-417. doi : 10.24033/bsmf.2540. http://www.numdam.org/articles/10.24033/bsmf.2540/

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