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Invariant measures for higher-rank hyperbolic abelian actions

Published online by Cambridge University Press:  19 September 2008

A. Katok  and
R. J. Spatzier
A. Katok
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
R. J. Spatzier
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48103, USA
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Abstract

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

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996 , pp. 751 - 778
Copyright
Copyright © Cambridge University Press 1996

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