The dynamics of quasi-isometric foliations

Details The dynamics of quasi-isometric foliations The dynamics of quasi-isometric foliations

2011-10-25

arxiv.org/abs/1110.5662v2

Mathematics

Dynamical Systems

18 pages, 1 figure

Scientific paper

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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