Recent results about stable ergodicity (Q2778780)

This survey is devoted to connections between partial hyperbolicity and ergodicity. The authors give an exposition of some recent results and ideas related to the following conjecture formulated by the second and third authors: on any compact manifold, ergodicity holds for an open and dense set of \(C^2\) volume preserving partially hyperbolic diffeomorphisms (provided that the stable and unstable subbundles are both nontrivial). Two related conjectures (connected with the notion of accessibility) are also formulated and discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0973.00044].