Invariant measures and stiffness for non Abelian groups of toral automorphisms

Let G be a non-elementary subgroup of SL_{2}(**Z**).
If *m* is a probability measure on **T**^{2}
which is G-invariant, then *m* 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 *m* is
*p*-stationary, i.e. *m*=*p***m*, where *p* is a
finitely supported probability measure on G whose support generates G.
The approach works more generally for G < SL_{d}(**Z**).

Bibliographical: C. R. Acad. Sci. Paris, Ser. I

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[Papers] [Alex Furman]