Positive Lyapunov Exponents for Quasiperiodic Szego cocycles

Details Positive Lyapunov Exponents for Quasiperiodic Szego cocycles Positive Lyapunov Exponents for Quasiperiodic Szego cocycles

2012-04-10

arxiv.org/abs/1204.2234v1

Mathematics

Dynamical Systems

27 papges

Scientific paper

In this paper we first obtain a formula of averaged Lyapunov exponents for ergodic Szego cocycles via the Herman-Avila-Bochi formula. Then using acceleration, we construct a class of analytic quasi-periodic Szego cocycles with uniformly positive Lyapunov exponents. Finally, a simple application of the main theorem in [Y] allows us to estimate the Lebesgue measure of support of the measure associated to certain class of C1 quasiperiodic 2- sided Verblunsky coefficients. Using the same method, we also recover the [S-S] results for Schrodinger cocycles with nonconstant real analytic potentials and obtain some nonuniform hyperbolicity results for arbitrarily fixed Brjuno frequency and for certain C1 potentials.

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