From a Gap in the Lyapunov Spectrum to Dominated Splittings

Let $A$ be an $α$-Hölder cocycle over a transitive two-sided subshift of finite type, and assume that $A$ is strongly bunched. We prove that if there exist $k\in\{1,\ldots,d-1\}$ and $c>0$ such that \[ λ_k(p)-λ_{k+1}(p)\ge c \] for every periodic point $p$, then $A$ admits a dominated splitting of