# American Institute of Mathematical Sciences

May  2010, 27(2): 609-615. doi: 10.3934/dcds.2010.27.609

## Rigidity of real-analytic actions of $SL(n,\Z)$ on $\T^n$: A case of realization of Zimmer program

 1 Department of Mathematics, Penn State University, University Park, State College, PA 16802 2 IMERL-Facultad de Ingeniería, Universidad de la República, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay

Received  February 2010 Published  February 2010

We prove that any real-analytic action of $SL(n,\Z),n\ge 3$ with standard homotopy data that preserves an ergodic measure $\mu$ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard linear action on the complement to a finite union of periodic orbits.
Citation: Anatole Katok, Federico Rodriguez Hertz. Rigidity of real-analytic actions of $SL(n,\Z)$ on $\T^n$: A case of realization of Zimmer program. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 609-615. doi: 10.3934/dcds.2010.27.609
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