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Partial hyperbolicity and classification: a survey

Published online by Cambridge University Press:  19 September 2016

ANDY HAMMERLINDL
Affiliation:
School of Mathematical Sciences, Monash University, Victoria 3800, Australia email andy.hammerlindl@monash.edu
RAFAEL POTRIE
Affiliation:
CMAT, Facultad de Ciencias, Universidad de la República, Uruguay email rpotrie@cmat.edu.uy
Corresponding

Abstract

This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group. Classification results in higher-dimensional settings are also discussed. The paper concludes with an overview of the construction of new partially hyperbolic examples derived from Anosov flows.

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Survey Article
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© Cambridge University Press, 2016 

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