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arXiv · 1302.0543

Pointwise partial hyperbolicity in 3-dimensional nilmanifolds

Andy Hammerlindl·Rafael Potrie
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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.

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Andy Hammerlindl, Rafael Potrie. 2013-02-03. Pointwise partial hyperbolicity in 3-dimensional nilmanifolds. https://doi.org/10.1112/jlms%2Fjdu013

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