Discontinuity of lyapunov exponents near fiber bunched cocycles

Clark Butler

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We give examples of locally constant -cocycles over a Bernoulli shift that are discontinuity points for Lyapunov exponents in the Hölder topology and are arbitrarily close to satisfying the fiber bunching inequality. Backes, Brown, and the author [Continuity of Lyapunov exponents for cocycles with invariant holonomies. Preprint, 2015, arXiv:1507.08978] have shown that the Lyapunov exponents vary continuously when restricted to the space of fiber bunched Hölder continuous cocycles. Our examples give evidence that this theorem is optimal within certain families of Hölder cocycles.

Original languageEnglish (US)
Pages (from-to)523-539
Number of pages17
JournalErgodic Theory and Dynamical Systems
Issue number2
StatePublished - Apr 1 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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