English

On conservative partially hyperbolic abelian actions with compact center foliation

Dynamical Systems 2017-06-13 v1

Abstract

We consider smooth partially hyperbolic volume preserving Z^k actions on smooth manifolds, with uniformly compact center foliation. We show that under certain irreducibility condition on the action, bunching and uniform quasiconformality conditions, the action is a smooth fiber bundle extension of an Anosov action, or the center foliation is pathological. We obtain several corollaries of this result. For example, we prove a global dichotomy result that any smooth conservative circle extension over a maximal Cartan action is either essentially a product of an action by rotations and a linear Anosov action on the torus, or has a pathological center foliation.

Keywords

Cite

@article{arxiv.1706.03626,
  title  = {On conservative partially hyperbolic abelian actions with compact center foliation},
  author = {Danijela Damjanovic and Disheng Xu},
  journal= {arXiv preprint arXiv:1706.03626},
  year   = {2017}
}