Skip to Main Content
Remote Access Electronic Research Announcements

Electronic Research Announcements

ISSN 1079-6762



Rigidity properties of $\mathbb {Z}^d$-actions on tori and solenoids

Authors: Manfred Einsiedler and Elon Lindenstrauss
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 99-110
MSC (2000): Primary 37A35; Secondary 37A45
Published electronically: October 14, 2003
MathSciNet review: 2029471
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that Haar measure is a unique measure on a torus or more generally a solenoid $X$ invariant under a not virtually cyclic totally irreducible $\mathbb Z^d$-action by automorphisms of $X$ 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Electronic Research Announcements of the American Mathematical Society with MSC (2000): 37A35, 37A45

Retrieve articles in all journals with MSC (2000): 37A35, 37A45

Additional Information

Manfred Einsiedler
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195
MR Author ID: 636562

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
MR Author ID: 605709

Keywords: Entropy, invariant measures, invariant $\sigma$-algebras, measurable factors, joinings, toral automorphisms, solenoid automorphism
Received by editor(s): July 12, 2003
Published electronically: 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
Article copyright: © Copyright 2003 American Mathematical Society