Rigidity of real-analytic actions of SL(n,ℤ) on τn: A case of realization of zimmer program

Anatole Katok; Federico Rodriguez Hertz

doi:10.3934/dcds.2010.27.609

Rigidity of real-analytic actions of SL(n,ℤ) on τⁿ: 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 ≥3 with standard homotopy data that preserves an ergodic measure u 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.

Original language	English (US)
Pages (from-to)	609-615
Number of pages	7
Journal	Discrete and Continuous Dynamical Systems
Volume	27
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2010.27.609
State	Published - Jun 2010

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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abstract = "We prove that any real-analytic action of SL(n, ℤ), n ≥3 with standard homotopy data that preserves an ergodic measure u 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.",

author = "Anatole Katok and Hertz, {Federico Rodriguez}",

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AB - We prove that any real-analytic action of SL(n, ℤ), n ≥3 with standard homotopy data that preserves an ergodic measure u 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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Rigidity of real-analytic actions of SL(n,ℤ) on τⁿ: A case of realization of zimmer program

Abstract

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