Rigidity of real-analytic actions of SL(n,ℤ) on τn

A case of realization of zimmer program

Anatoly Katok, Federico Juan Rodriguez Hertz

Research output: Contribution to journal › Article

5 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)609-615
Number of pages7
JournalDiscrete and Continuous Dynamical Systems
Volume27
Issue number2
DOIs
StatePublished - Jun 1 2010

Fingerprint

Rigidity
Ergodic Measure
Invariant Set
Open set
Periodic Orbits
Homotopy
Orbits
Ball
Union
Complement
Standards

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Katok, Anatoly ; Rodriguez Hertz, Federico Juan. / Rigidity of real-analytic actions of SL(n,ℤ) on τn : A case of realization of zimmer program. In: Discrete and Continuous Dynamical Systems. 2010 ; Vol. 27, No. 2. pp. 609-615.
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Katok, A & Rodriguez Hertz, FJ 2010, 'Rigidity of real-analytic actions of SL(n,ℤ) on τn: A case of realization of zimmer program', Discrete and Continuous Dynamical Systems, vol. 27, no. 2, pp. 609-615. https://doi.org/10.3934/dcds.2010.27.609

Rigidity of real-analytic actions of SL(n,ℤ) on τn : A case of realization of zimmer program. / Katok, Anatoly; Rodriguez Hertz, Federico Juan.

In: Discrete and Continuous Dynamical Systems, Vol. 27, No. 2, 01.06.2010, p. 609-615.

Research output: Contribution to journal › Article

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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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Katok A, Rodriguez Hertz FJ. Rigidity of real-analytic actions of SL(n,ℤ) on τn: A case of realization of zimmer program. Discrete and Continuous Dynamical Systems. 2010 Jun 1;27(2):609-615. https://doi.org/10.3934/dcds.2010.27.609

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