Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T17:27:11.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Lyapunov exponents for some quasi-periodic cocycles

Published online by Cambridge University Press:  17 April 2001

L.-S. YOUNG
L.-S. YOUNG
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider $SL(2, {\Bbb R} )$-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents $\approx \pm \log \lambda $ if the norms of all of the matrices are $\approx \lambda $. This is proved for $\lambda $ sufficiently large. The ubiquity of elliptic behavior is also observed.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 2 , April 1997 , pp. 483 - 504
Copyright
1997 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research is partially supported by the National Science Foundation.