Continuity of the Lyapunov exponent for analytic multi-frequency quasi-periodic cocycles

Math Physics Seminar
Thursday, January 12, 2023 - 12:00pm for 1 hour (actually 50 minutes)
Skiles Room 005
Matthew Powell – School of Mathematics, Georgia Tech –
Michael Loss

The purpose of this talk is to discuss our recent work on multi-frequency quasi-periodic cocycles, establishing continuity (both in cocycle and jointly in cocycle and frequency) of the Lyapunov exponent for non-identically singular cocycles. Analogous results for one-frequency cocycles have been known for over a decade, but the multi-frequency results have been limited to either Diophantine frequencies (continuity in cocycle) or SL(2,C) cocycles (joint continuity). We will discuss the main points of our argument, which extends earlier work of Bourgain.