Invariant measures and stiffness for non-Abelian groups of toral automorphisms

Jean Bourgain*, Alex Furman, Elon Lindenstrauss, Shahar Mozes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Let Γ be a non-elementary subgroup of SL2 (Z). If μ is a probability measure on T2 which is Γ-invariant, then μ is a convex combination of the Haar measure and an atomic probability measure supported by rational points. The same conclusion holds under the weaker assumption that μ is ν-stationary, i.e. μ = ν * μ, where ν is a finitely supported, probability measure on Γ whose support suppν generates Γ. The approach works more generally for Γ < SLd (Z). To cite this article: J. Bourgain et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

Original languageAmerican English
Pages (from-to)737-742
Number of pages6
JournalComptes Rendus Mathematique
Issue number12
StatePublished - 15 Jun 2007

Bibliographical note

Funding Information:
✩ This research is supported in part by NSF DMS grants 0627882 (JB), 0604611 (AF), 0500205 & 0554345 (EL) and BSF grant 2004-010 (SM).


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