Abstract
AbstractWe 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.