Mathematische Zeitschrift

, 263:221 | Cite as

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 \({{\rm GL}(d, \mathbb R)}\) 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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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Pontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil
  2. 2.IMPARio de JaneiroBrazil
  3. 3.IMBUniversité de Bordeaux IBordeauxFrance

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