The dynamics of quasi-isometric foliations

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.

18 pages, 1 figure

References in corpus (2)

• On 3-manifolds that support partially hyperbolic diffeomorphisms
• Partial hyperbolicity on 3-dimensional nilmanifolds

Cited by in corpus (5)

• Partial hyperbolicity and classification: a survey
• Partial hyperbolicity and attracting regions in 3-dimensional manifolds
• Equilibrium states for partially hyperbolic maps with one-dimensional center
• Polynomial Global Product Structure
• On expanding foliations