Partial hyperbolicity and classification: a survey
Andy Hammerlindl, Rafael Potrie
TL;DR
This survey reviews recent advances in classifying partially hyperbolic diffeomorphisms, focusing on branching foliations, leaf conjugacies, and new examples derived from Anosov flows across various dimensions.
Contribution
It compiles recent classification results, construction methods, and extends understanding of partially hyperbolic systems in multiple dimensions.
Findings
Construction of branching foliations on 3-manifolds
Classification results for higher-dimensional systems
New examples from Anosov flows
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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