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arXiv · 2210.09285

Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles

Matthew Powell
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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 $M(2,\mathbb{C})$ cocycles. Our corollaries include applications to multifrequency Jacobi cocycles with periodic background potentials.

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BibTeXRIS

Matthew Powell. 2022-10-17. Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles. https://arxiv.org/abs/2210.09285

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