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arXiv · 1002.2942

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

Anatole Katok·Federico Rodriguez Hertz
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Abstract

We prove that any real-analytic action of $SL(n,\Z), n\ge 3$ with standard homotopy data that preserves an ergodic measure $μ$ 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.

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Anatole Katok, Federico Rodriguez Hertz. 2010-02-15. Rigidity of real-analytic actions of $SL(n,\Z)$ on $\T^n$: A case of realization of Zimmer program. https://arxiv.org/abs/1002.2942

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