TY - JOUR
T1 - A geometric path from zero Lyapunov exponents to rotation cocycles
AU - Bochi, Jairo
AU - Navas, Andrés
N1 - Publisher Copyright:
© Cambridge University Press, 2013.
PY - 2015/9/11
Y1 - 2015/9/11
N2 - We consider cocycles of isometries on spaces of non-positive curvature H. We show that the supremum of the drift over all invariant ergodic probability measures equals the infimum of the displacements of continuous sections under the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift, then there are almost invariant sections, that is, sections that move arbitrarily little under the cocycle dynamics. If, in addition, H is a symmetric space, then we show that almost invariant sections can be made invariant by perturbing the cocycle.
AB - We consider cocycles of isometries on spaces of non-positive curvature H. We show that the supremum of the drift over all invariant ergodic probability measures equals the infimum of the displacements of continuous sections under the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift, then there are almost invariant sections, that is, sections that move arbitrarily little under the cocycle dynamics. If, in addition, H is a symmetric space, then we show that almost invariant sections can be made invariant by perturbing the cocycle.
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U2 - 10.1017/etds.2013.58
DO - 10.1017/etds.2013.58
M3 - Article
AN - SCOPUS:84912151155
SN - 0143-3857
VL - 35
SP - 374
EP - 402
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 2
ER -