The fibered rotation number for ergodic symplectic cocycles and its applications: I. Gap Labelling Theorem

Xianzhe Li, Li Wu

Let $(\Theta ,T,\mu )$ be an ergodic topological dynamical system. The fibered rotation number for cocycles in $\Theta \times \mathrm{SL}(2,\mathbb{R})$, acting on $ Θ\times \mathbb{R}\mathbb…