Partial hyperbolicity and classification: a survey

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.

49 pages, 6 figures

References in corpus (3)

• A non-dynamically coherent example on ${\mathbb{T}}^3$
• Partially hyperbolic dynamics in dimension 3
• Aspherical products which do not support Anosov diffeomorphisms

Cited by in corpus (2)

• Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence
• Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center