English

Pointwise partial hyperbolicity in 3-dimensional nilmanifolds

Dynamical Systems 2017-05-17 v1 Geometric Topology

Abstract

We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further classify the partially hyperbolic systems on these manifolds up to leaf conjugacy. We also classify those systems on the 3-torus which do not have an attracting or repelling periodic 2-torus. These classification results allow us to prove some dynamical consequences, including existence and uniqueness results for measures of maximal entropy and quasi-attractors.

Keywords

Cite

@article{arxiv.1302.0543,
  title  = {Pointwise partial hyperbolicity in 3-dimensional nilmanifolds},
  author = {Andy Hammerlindl and Rafael Potrie},
  journal= {arXiv preprint arXiv:1302.0543},
  year   = {2017}
}

Comments

28 pages, 1 figure

R2 v1 2026-06-21T23:20:00.394Z