3 papers
math.DS2025
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 -cocycles for fixed irrational frequencies. Especially, we prov…
math.DS2019
Large Deviation theorems for Dirichlet determinants of analytic quasi-periodic Jacobi operators with Brjuno-Rüssmann frequency
Wenmeng Geng, Kai Tao
In this paper, we first study the strong Birkhoff Ergodic Theorem for subharmonic functions with the Brjuno-Rüssmann shift on the Torus. Then, we apply it to prove the large deviat…
math.DS2018
Strong Birkhoff Ergodic Theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles
Kai Tao
In this paper, we first prove the strong Birkhoff Ergodic Theorem for subharmonic functions with the irrational shift on the Torus. Then, it is applied to the analytic quasi-period…