Electronic Research Announcements

Author(s): Manfred Einsiedler; Elon Lindenstrauss
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 99-110.
MSC (2000): Primary 37A35; Secondary 37A45
Posted: October 14, 2003
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Abstract: We show that Haar measure is a unique measure on a torus or more generally a solenoid

invariant under a not virtually cyclic totally irreducible $\mathbb Z^d$ -action by automorphisms of

such that at least one element of the action acts with positive entropy. We also give a corresponding theorem in the non-irreducible case. These results have applications regarding measurable factors and joinings of these algebraic $\mathbb Z^d$ -actions.

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Retrieve articles in Electronic Research Announcements with MSC (2000): 37A35, 37A45

Manfred Einsiedler
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195
Email: einsiedl@math.washington.edu

Elon Lindenstrauss
Affiliation: Department of Mathematics, Stanford University, Stanford, CA 94305
Address at time of publication: Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012
Email: elonbl@member.ams.org

DOI: 10.1090/S1079-6762-03-00117-3
PII: S 1079-6762(03)00117-3
Keywords: Entropy, invariant measures, invariant $\sigma$-algebras, measurable factors, joinings, toral automorphisms, solenoid automorphism
Received by editor(s): July 12, 2003
Posted: October 14, 2003
Additional Notes: E.L. is supported in part by NSF grant DMS-0140497. The two authors gratefully acknowledge the hospitality of Stanford University and the University of Washington, respectively
Communicated by: Klaus Schmidt
Copyright of article: Copyright 2003, American Mathematical Society

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