Some Characterizations of Domination

Details Some Characterizations of Domination Some Characterizations of Domination

2008-08-28

arxiv.org/abs/0808.3811v2

Mathematische Zeitschrift, 263, no. 1 (2009), 221-231

Mathematics

Dynamical Systems

10 pages, 2 figures; acknowledgements added

Scientific paper

10.1215/00127094-2008-065

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 $\Sigma$ in $GL(d,\mathbb{R})$ with the property that any cocycle with values in $\Sigma$ has a dominated splitting. We characterize these sets in terms of existence of invariant multicones, thus extending a 2-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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