### 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 |

State | Published - Apr 1997 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Ergodic Theory and Dynamical Systems*,

*17*(2), 483-504.

**Lyapunov exponents for some quasi-periodic cocycles.** / Young, L. S.

Research output: Contribution to journal › Article

*Ergodic Theory and Dynamical Systems*, vol. 17, no. 2, pp. 483-504.

}

TY - JOUR

T1 - Lyapunov exponents for some quasi-periodic cocycles

AU - Young, L. S.

PY - 1997/4

Y1 - 1997/4

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0031534023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031534023&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031534023

VL - 17

SP - 483

EP - 504

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 2

ER -