Cocycles with one exponent over partially hyperbolic systems
Dynamical Systems
2012-09-11 v2
Abstract
We consider Holder continuous linear cocycles over partially hyperbolic diffeomorphisms. For fiber bunched cocycles with one Lyapunov exponent we show continuity of measurable invariant conformal structures and sub-bundles. Further, we establish a continuous version of Zimmer's Amenable Reduction Theorem. For cocycles over hyperbolic systems we also obtain polynomial growth estimates for the norm and quasiconformal distortion from the periodic data.
Cite
@article{arxiv.1111.3400,
title = {Cocycles with one exponent over partially hyperbolic systems},
author = {Boris Kalinin and Victoria Sadovskaya},
journal= {arXiv preprint arXiv:1111.3400},
year = {2012}
}
Comments
Theorem 3.4 corrected; Corollary 3.8, Theorem 3.9, and Example 4.6 added