TY - JOUR
T1 - Some characterizations of domination
AU - Bochi, Jairo
AU - Gourmelon, Nicolas
N1 - Funding Information:
J. Bochi and N. Gourmelon were partially supported by CNPq (Brazil).
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
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U2 - 10.1007/s00209-009-0494-y
DO - 10.1007/s00209-009-0494-y
M3 - Article
AN - SCOPUS:70350006992
SN - 0025-5874
VL - 263
SP - 221
EP - 231
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1
ER -