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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
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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

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Footnotes

This research is partially supported by the National Science Foundation.