TY - JOUR
T1 - Discontinuity of lyapunov exponents near fiber bunched cocycles
AU - Butler, Clark
N1 - Publisher Copyright:
© Cambridge University Press, 2016.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/4/1
Y1 - 2018/4/1
N2 - 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.
AB - 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.
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U2 - 10.1017/etds.2016.56
DO - 10.1017/etds.2016.56
M3 - Article
AN - SCOPUS:84988422326
VL - 38
SP - 523
EP - 539
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 2
ER -