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

Dynamical Systems 2022-10-18 v1 Mathematical Physics math.MP Spectral Theory

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

Keywords

Cite

@article{arxiv.2210.09285,
  title  = {Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles},
  author = {Matthew Powell},
  journal= {arXiv preprint arXiv:2210.09285},
  year   = {2022}
}