English

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.

Keywords

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

R2 v1 2026-06-21T19:36:07.009Z