Speaker:
Christian Sadel
Institution:
UBC
Time:
Thursday, February 21, 2013 - 2:00pm
Location:
RH 306
We consider analytic cocycles of d \times d matrices. Such cocycles
appear for instance for the transfer matrices of a quasi periodic
Schrödinger operator on a strip.
We prove joint continuity (depending on frequency and the analytic
function of d \times d matrices) of all Lyapunov exponents at irrational
frequencies. Moreover, the so called accelerations (previously defined
for SL(2,C) cocycles by A. Avila) are also quantized at irrational
frequencies.
As a consequence, we obtain that the set of dominated cocycles is dense
within the set of cocycles where one has at least 2 different Lyapunov
exponents.
joint work with A. Avila and S. Jitomirskaya