Leaf conjugacies on the torus

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Abstract

If a partially hyperbolic diffeomorphism on a torus of dimension d?3 has stable and unstable foliations which are quasi-isometric on the universal cover, and its centre direction is one-dimensional, then the diffeomorphism is leaf conjugate to a linear toral automorphism. In other words, the hyperbolic structure of the diffeomorphism is exactly that of a linear, and thus simple to understand, example. In particular, every partially hyperbolic diffeomorphism on the 3-torus is leaf conjugate to a linear toral automorphism.
Original languageEnglish
Pages (from-to)896 - 933
Number of pages38
JournalErgodic Theory and Dynamical Systems
Volume33
Issue number3
DOIs
Publication statusPublished - 2013
Externally publishedYes

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