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Continuity of Lyapunov exponents in the C0 topology

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Abstract

We prove that the Bochi–Mañé theorem is false, in general, for linear cocycles over non-invertible maps: there are C0-open subsets of linear cocycles that are not uniformly hyperbolic and yet have Lyapunov exponents bounded from zero.

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Authors and Affiliations

  1. IMPA, Est. D. Castorina 110, 22460-320, Rio de Janeiro, Brazil

    Marcelo Viana

  2. Departamento de Geometria, Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, Brazil

    Jiagang Yang

Authors
  1. Marcelo Viana
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  2. Jiagang Yang
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Corresponding author

Correspondence to Marcelo Viana.

Additional information

Partially supported by Fondation Louis D.—Institut de France (project coordinated by M. Viana), CNPq and FAPERJ

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Viana, M., Yang, J. Continuity of Lyapunov exponents in the C0 topology. Isr. J. Math. 229, 461–485 (2019). https://doi.org/10.1007/s11856-018-1809-7

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  • DOI: https://doi.org/10.1007/s11856-018-1809-7

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