Characterization of uniform hyperbolicity for fibre-bunched cocycles. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Velozo Ruiz, Renato
• Is Part Of: Dynamical systems. Volume 35:Issue 1(2020)
• Page Start: 124
• Page End: 139
• Publication Date: 2020-01-02
• Subjects: Cocycles -- uniform hyperbolicity -- fiber-bunched -- Lyapunov exponents -- gap; 37D20; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1649364
• Languages: English
• ISSNs: 1468-9367

Abstract

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.