Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles
Abstract
It is known that the Lyapunov exponent of analytic 1-frequency quasiperiodic cocycles is continuous in cocycle and, when the frequency is irrational, jointly in cocycle and frequency. In this paper, we extend a result of Bourgain to show the same continuity result for multifrequency quasiperiodic M(2,C) cocycles. Our corollaries include applications to multifrequency Jacobi cocycles with periodic background potentials.
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