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Leaf conjugacies on the torus

Published online by Cambridge University Press:  29 January 2013

ANDY HAMMERLINDL
ANDY HAMMERLINDL*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4 email andy@math.utoronto.ca
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Abstract

If a partially hyperbolic diffeomorphism on a torus of dimension $d\geq 3$ 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 3 , June 2013 , pp. 896 - 933
Copyright
Copyright ©2013 Cambridge University Press

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