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

Authors
  • Katok, Anatole
  • Hertz, Federico Rodriguez
Type
Preprint
Publication Date
Feb 15, 2010
Submission Date
Feb 15, 2010
Source
arXiv
License
Yellow
External links

Abstract

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.

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