Stable ergodicity and julienne quasi-conformality
This paper is devoted to the improvement in our understanding of the properties of the (un)stable manifold foliations. To this end the authors introduce new concepts -- julienne density and julienne quasi-conformality. They prove, based on center bunching conditions, that the holonomy maps of strong (un)stable foliations are julienne quasi-conformal and hence preserve all julienne density points. As a consequence they markedly expand the class of known stably ergodic diffeomorphisms. In particular, they show that all affine diffeomorphisms of compact homogeneous spaces with the accessibility property are stably ergodic.
scientific article; zbMATH DE number 1454679