TY - JOUR
T1 - Invariant measures and stiffness for non-Abelian groups of toral automorphisms
AU - Bourgain, Jean
AU - Furman, Alex
AU - Lindenstrauss, Elon
AU - Mozes, Shahar
N1 - 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).
PY - 2007/6/15
Y1 - 2007/6/15
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=34447341450&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2007.04.017
DO - 10.1016/j.crma.2007.04.017
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AN - SCOPUS:34447341450
SN - 1631-073X
VL - 344
SP - 737
EP - 742
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 12
ER -