Skip to main content Accessibility help
×
Home

Discontinuity of Lyapunov exponents near fiber bunched cocycles

  • CLARK BUTLER (a1)

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.

Copyright

References

Hide All
[1] Abadi, M. and Vergne, N.. Sharp error terms for return time statistics under mixing conditions. J. Theoret. Probab. 22(1) (2009), 1837.
[2] Backes, L., Brown, A. and Butler, C.. Continuity of Lyapunov exponents for cocycles with invariant holonomies. Preprint, 2015, arXiv:1507.08978.
[3] Bochi, J.. Genericity of zero Lyapunov exponents. Ergod. Th. & Dynam. Sys. 22 (2002), 16671696.
[4] Bocker-Neto, C. and Viana, M.. Continuity of Lyapunov exponents for random 2d matrices. Ergod. Th. & Dynam. Sys., to appear, Preprint, 2010, arXiv:1012.0872.
[5] Tao, T.. Topics in Random Matrix Theory (Graduate Studies in Mathematics, 132) . American Mathematical Society, Providence, RI, 2012.
[6] Viana, M.. Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. Ann. of Math. (2) 167(2) (2008), 643680.
[7] Viana, M.. Lectures on Lyapunov Exponents (Cambridge Studies in Advanced Mathematics, 145) . Cambridge University Press, Cambridge, 2014.

Related content

Powered by UNSILO

Discontinuity of Lyapunov exponents near fiber bunched cocycles

  • CLARK BUTLER (a1)

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.