Lyapunov exponents for some quasi-periodic cocycles

L. S. Young

doi:10.1017/S0143385797079170

Lyapunov exponents for some quasi-periodic cocycles

L. S. Young

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider SL(2, ℝ)-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents ≈ ±logλ if the norms of all of the matrices are ≈ λ. This is proved for λ sufficiently large. The ubiquity of elliptic behavior is also observed. † This research is partially supported by the National Science Foundation.

Original language	English (US)
Pages (from-to)	483-504
Number of pages	22
Journal	Ergodic Theory and Dynamical Systems
Volume	17
Issue number	2
DOIs	https://doi.org/10.1017/S0143385797079170
State	Published - Apr 1997

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1017/S0143385797079170

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abstract = "We consider SL(2, ℝ)-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents ≈ ±logλ if the norms of all of the matrices are ≈ λ. This is proved for λ sufficiently large. The ubiquity of elliptic behavior is also observed. † This research is partially supported by the National Science Foundation.",

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AB - We consider SL(2, ℝ)-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents ≈ ±logλ if the norms of all of the matrices are ≈ λ. This is proved for λ sufficiently large. The ubiquity of elliptic behavior is also observed. † This research is partially supported by the National Science Foundation.

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Lyapunov exponents for some quasi-periodic cocycles

Abstract

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