Abstract

We show that the set of cocycles with integral separateness is open and dense in the space of all bounded \(\text{GL}(d,{\mathbb R})\)-cocycles equipped with uniform topology. As a consequence, a generic bounded linear cocycle has simple Lyapunov spectrum and dominated Oseledets splitting, and a generic bounded \(\text{SL}(2,\mathbb R)\)-cocycle is uniformly hyperbolic.