Mathematical Research Letters

Volume 25 (2018)

Number 6

The set of fiber-bunched cocycles with nonvanishing Lyapunov exponents over a partially hyperbolic map is open

Pages: 1719 – 1740

DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n6.a2

Authors

Lucas Backes (Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil)

Mauricio Poletti (LAGA, Université Paris 13, Villetaneus, France)

Adriana Sánchez (IMPA, Rio de Janeiro, RJ, Brazil)

Abstract

We prove that the set of fiber-bunched $SL(2, \mathbb{R})$-valued Hölder cocycles with nonvanishing Lyapunov exponents over a volume preserving, accessible and center-bunched partially hyperbolic diffeomorphism is open. Moreover, we present an example showing that this is no longer true if we do not assume accessibility in the base dynamics.

Received 3 July 2017

Published 25 March 2019