Duke Mathematical Journal
- Duke Math. J.
- Volume 161, Number 7 (2012), 1305-1350.
Topological self-joinings of Cartan actions by toral automorphisms
We show that if and is a faithful -Cartan action on a torus by automorphisms, then any closed subset of which is invariant and topologically transitive under the diagonal -action by is homogeneous, in the sense that it is either the full torus , or a finite set of rational points, or a finite disjoint union of parallel translates of some -dimensional invariant subtorus. A counterexample is constructed for the rank case.
Duke Math. J., Volume 161, Number 7 (2012), 1305-1350.
First available in Project Euclid: 4 May 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]
Secondary: 37A45: Relations with number theory and harmonic analysis [See also 11Kxx]
Lindenstrauss, Elon; Wang, Zhiren. Topological self-joinings of Cartan actions by toral automorphisms. Duke Math. J. 161 (2012), no. 7, 1305--1350. doi:10.1215/00127094-1593290. https://projecteuclid.org/euclid.dmj/1336142077