Abstract
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 \({{\rm GL}(d, \mathbb R)}\) 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.
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J. Bochi and N. Gourmelon were partially supported by CNPq (Brazil).
An erratum to this article can be found at http://dx.doi.org/10.1007/s00209-009-0516-9
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Bochi, J., Gourmelon, N. Some characterizations of domination. Math. Z. 263, 221–231 (2009). https://doi.org/10.1007/s00209-009-0494-y
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DOI: https://doi.org/10.1007/s00209-009-0494-y