On the ergodicity of partially hyperbolic systems

Keith Burns; Amie Wilkinson

On the ergodicity of partially hyperbolic systems

Dynamical Systems 2007-05-23 v1

Authors: Keith Burns , Amie Wilkinson

Abstract

Pugh and Shub have conjectured that essential accessibility implies ergodicity, for a $C^2$ , partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satsified by all partially hyperbolic systems with 1-dimensional center bundle. We also obtain ergodicity results for $C^{1+\gamma}$ partially hyperbolic systems.

Keywords

partially hyperbolic dynamics hyperbolic geometry hyperbolic groups

Cite

@article{arxiv.math/0510234,
  title  = {On the ergodicity of partially hyperbolic systems},
  author = {Keith Burns and Amie Wilkinson},
  journal= {arXiv preprint arXiv:math/0510234},
  year   = {2007}
}

Comments

46 pages, 4 figures

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