Stable Ergodicity and Julienne Quasi-Conformality

        In this paper we eliminate some of the most nettlesome hypotheses of our previous article, "Stably ergodic dynamical systems and partial hyperbolicity" [22], and expand the domain of stably ergodic, partially hyperbolic dynamical systems to include all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property. Our main tool is a new concept -- julienne quasi-conformality of the stable and unstable holonomy maps. An important feature of this is that the holonomy maps preserve all julienne density points.

By: Charles Pugh, Michael Shub

Published in: RC20981 in 1997


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