Discontinuity of Lyapunov exponent in spaces of quasiperiodic cocycles: Smoothness vs Arithmetic

Jinhao Liang, Kai Tao, Jiangong You

We construct examples of discontinuity of Lyapunov exponent in the spaces of quasiperiodic $\mathrm{SL}(2,\mathbb{R})$-cocycles for fixed irrational frequencies. Especially, we prov…