Examples of Discontinuity of Lyapunov Exponent in Smooth Quasi-Periodic Cocycles

Yiqian Wang, Jiangong You

We study the regularity of the Lyapunov exponent for quasi-periodic cocycles $(T_{\omega },A)$ where $T_{\omega }$ is an irrational rotation $x\to x+2\pi \omega$ on $\SS^1$ and $A\in {\cal C}^l(\SS^1, S…