Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents

• Autores: Marcelo Viana
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 167, Nº 2, 2008, págs. 643-680
• Idioma: inglés
• DOI: 10.4007/annals.2008.167.643
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• Resumen

  • We prove that for any s > 0 the majority of Cs 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-8. 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.