A geometric path from zero Lyapunov exponents to rotation cocycles
Abstract
We consider cocycles of isometries on spaces of nonpositive curvature . 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, is a symmetric space, then we show that almost invariant sections can be made invariant by perturbing the cocycle.
Cite
@article{arxiv.1112.0397,
title = {A geometric path from zero Lyapunov exponents to rotation cocycles},
author = {Jairo Bochi and Andrés Navas},
journal= {arXiv preprint arXiv:1112.0397},
year = {2019}
}
Comments
To appear in Ergodic Theory and Dynamical Systems. The title was reverted to a previous one. Some modifications were made according to the referee's suggestions. We also included an alternative proof of Theorem A