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arXiv · 1110.5662

The dynamics of quasi-isometric foliations

Andy Hammerlindl
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Abstract

If the stable, center, and unstable foliations of a partially hyperbolic system are quasi-isometric, the system has Global Product Structure. This result also applies to Anosov systems and to other invariant splittings. If a partially hyperbolic system on a manifold with abelian fundamental group has quasi-isometric stable and unstable foliations, the center foliation is without holonomy. If, further, the system has Global Product Structure, then all center leaves are homeomorphic.

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Andy Hammerlindl. 2012-03-23. The dynamics of quasi-isometric foliations. https://doi.org/10.1088/0951-7715%2F25%2F6%2F1585

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