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Some results on $d \times d$ cocycles

Presented by: 
C Sadel Institute of Science and Technology (IST Austria)
Date: 
Thursday 19th March 2015 - 12:30 to 13:30
Venue: 
INI Seminar Room 2
Abstract: 
I want to present some results on higher dimensional cocycles which may have applications for quasi-periodic operators on strips. The talk is split into two parts:

1.) On complex analytic one-frequency cocycles (joint work with A. Avila and S. Jitomirskaya) We classify dominated cocycles and show joint continuity in frequency and analytic cocycle function A(x) of all Lyapunov exponents at irrational frequencies. As a consequence we also obtain that for a given frequency there is a dense open set of cocycles that are odminated or have trivial Lyapunov spectrum.

2.) A Herman-Avila-Bochi formula for Hermitian symplectic or pseudo-unitary cocycles. I show a generalization of the Herman-Avila Bochi formula for SL(2,R) cocycles.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons