Mathematische Zeitschrift

, 263:221 | Cite as

Some characterizations of domination

Article

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.

Keywords

Vector Bundle Lyapunov Exponent Exponential Dichotomy Convexity Property Strict Invariance 
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Copyright information

© 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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