TL;DR
This paper reviews recent advances in the study of volume-preserving partially hyperbolic diffeomorphisms, focusing on ergodicity, accessibility, Lyapunov exponents, foliations, and rigidity, highlighting their interconnections.
Contribution
It synthesizes recent progress and explores the relationships between key dynamical properties in volume-preserving partially hyperbolic systems.
Findings
Density of stable ergodicity established
Stable accessibility results discussed
Connections between rigidity and foliations analyzed
Abstract
We discuss recent progress in understanding the dynamical properties of partially hyperbolic diffeomorphisms that preserve volume. The main topics addressed are density of stable ergodicity and stable accessibility, center Lyapunov exponents, pathological foliations, rigidity, and the surprising interrelationships between these notions.
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