Ergodic Theory and Dynamical Systems

Survey Article

Invariant measures for higher-rank hyperbolic abelian actions

A. Katoka1 and R. J. Spatziera2

a1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA

a2 Department of Mathematics, University of Michigan, Ann Arbor, MI 48103, USA

Abstract

We investigate invariant ergodic measures for certain partially hyperbolic and Anosov actions of k, k and We show that they are either Haar measures or that every element of the action has zero metric entropy.

(Received June 25 1992)

(Revised February 15 1995)

Footnotes

† Partially supported by NSF grant DMS 9017995.

‡ Partially supported by the NSF, AMS Centennial Fellow.