Characterization of uniform hyperbolicity for fibre-bunched cocycles. Issue 1 (2nd January 2020) - Velozo Ruiz, Renato
ABSTRACT: We prove a new characterization of uniform hyperbolicity for fibre-bunched cocycles. Specifically, we show that the existence of a uniform gap between the Lyapunov exponents of a fibre-bunched S L ( 2, R ) -cocycle defined over a subshift of finite type or an Anosov diffeomorphism implies uniform hyperbolicity. In addition, we construct an α -Hölder cocycle which has a uniform gap between the Lyapunov exponents, however, it is not uniformly hyperbolic.