Some characterizations of domination

Jairo Bochi, Nicolas Gourmelon

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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 GL(d, 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.

Original languageEnglish (US)
Pages (from-to)221-231
Number of pages11
JournalMathematische Zeitschrift
Volume263
Issue number1
DOIs
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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