Some characterizations of domination

We show that a cocycle has a dominated splitting if and only if there is a uniform exponential gap between singular values of its iterates. Then we consider sets Σ in with the property that any cocycle with values in Σ has a dominated splitting. We characterize these sets in terms of existence of invariant multicones, thus extending a two-dimensional result by Avila, Bochi, and Yoccoz. We give an example showing how these multicones can fail to have convexity properties. J. Bochi and N. Gourmelon were partially supported by CNPq (Brazil). An erratum to this article can be found at