2018/07/30 by Velozo, Renato
#37D20 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1807.11335
We prove a new characterization of uniform hyperbolicity for fiber-bunched cocycles. Specifically, we show that the existence of a uniform gap between the Lyapunov exponents of a fiber-bunched SL(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 uniform gap between the Lyapunov exponents, however it is not uniformly hyperbolic.