Speaker: Svetlana Jitomirskaya (UC-Irvine)
Title: Analytic quasiperiodic cocycles
Time: Today (Friday, Feb 21) at 4PM in Van Vleck B239

Abstract:

Analytic quasiperiodic matrix cocycles is a simple dynamical system, where
analytic and dynamical properties are related in an unexpected and
remarkable way. We will focus on this relation, leading to a new approach to
the proof of joint continuity of Lyapunov exponents in frequency and
cocycle, at irrational frequency, first proved for SL(2,C) cocycles in
Bourgain-Jitom., 2002. The approach is powerful enough to handle singular
and multidimensional cocycles, thus establishing the above continuity in
full generality. This has important consequences including a dense open
version of Bochi-Viana theorem in this setting, with a completely different
underlying mechanism of the proof. A large part of the talk is a report on a
joint work with A. Avila and C. Sadel.