Reducibility, differentiable rigidity and Lyapunov exponents for quasi-periodic cocycles on $\mathbf{T}timesSL(2,\mathbf{R})$

Raphaël Krikorian

Given $\alpha$ in some set $\Sigma$ of total (Haar) measure in $\mathbf{T}=\mathbf{R}/\mathbf{Z}$, and $A\in C^{\infty }(\mathbf{T},SL(2,\mathbf{R}))$ which is homotopic to the identity, we prove that if th…