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Partial hyperbolicity and classification: a survey

Published online by Cambridge University Press:  19 September 2016

ANDY HAMMERLINDL  and
RAFAEL POTRIE
ANDY HAMMERLINDL
Affiliation:
School of Mathematical Sciences, Monash University, Victoria 3800, Australia email [email protected]
RAFAEL POTRIE
Affiliation:
CMAT, Facultad de Ciencias, Universidad de la República, Uruguay email [email protected]
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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.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 2 , April 2018 , pp. 401 - 443
Copyright
© Cambridge University Press, 2016 

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