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.
ASJC Scopus subject areas
- Applied Mathematics