Dynamics of quasi-isometric foliations

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Abstract

If the stable, centre 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 an abelian fundamental group has quasi-isometric stable and unstable foliations, the centre foliation is without holonomy. If, further, the system has Global Product Structure, then all centre leaves are homeomorphic.
Original languageEnglish
Pages (from-to)1585 - 1599
Number of pages15
JournalNonlinearity
Volume25
Issue number6
DOIs
Publication statusPublished - 2012
Externally publishedYes

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