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Discontinuity of Lyapunov exponents near fiber bunched cocycles

Published online by Cambridge University Press:  19 September 2016

CLARK BUTLER
CLARK BUTLER*
Affiliation:
Department of Mathematics, The University of Chicago, 5734 S University Ave, Chicago, IL 60637, USA email cbutler@math.uchicago.edu
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Abstract

We give examples of locally constant $\text{SL}(2,\mathbb{R})$-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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 2 , April 2018 , pp. 523 - 539
Copyright
© Cambridge University Press, 2016 

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