### Abstract

We make a modest progress in the nonuniform measure rigidity program started in 2007 and its applications to the Zimmer program. The principal innovation is in establishing rigidity of large measures for actions of ℤ^{k}, k ≥ 2 with pairs of negatively proportional Lyapunov exponents which translates to applicability of our results to actions of lattices in higher rank semisimple Lie groups other than SL(n, ℝ), namely, Sp(2n, ℤ) and SO(n, n; ℤ).

Original language | English (US) |
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Title of host publication | Contemporary Mathematics |

Publisher | American Mathematical Society |

Pages | 195-208 |

Number of pages | 14 |

DOIs | |

State | Published - Jan 1 2017 |

### Publication series

Name | Contemporary Mathematics |
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Volume | 692 |

ISSN (Print) | 0271-4132 |

ISSN (Electronic) | 1098-3627 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

^{k}actions of symplectic type. In

*Contemporary Mathematics*(pp. 195-208). (Contemporary Mathematics; Vol. 692). American Mathematical Society. https://doi.org/10.1090/conm/692/13923

}

^{k}actions of symplectic type. in

*Contemporary Mathematics.*Contemporary Mathematics, vol. 692, American Mathematical Society, pp. 195-208. https://doi.org/10.1090/conm/692/13923

**Non-uniform measure rigidity for ℤ ^{k} actions of symplectic type.** / Katok, Anatole; Hertz, Federico Rodriguez.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Non-uniform measure rigidity for ℤk actions of symplectic type

AU - Katok, Anatole

AU - Hertz, Federico Rodriguez

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We make a modest progress in the nonuniform measure rigidity program started in 2007 and its applications to the Zimmer program. The principal innovation is in establishing rigidity of large measures for actions of ℤk, k ≥ 2 with pairs of negatively proportional Lyapunov exponents which translates to applicability of our results to actions of lattices in higher rank semisimple Lie groups other than SL(n, ℝ), namely, Sp(2n, ℤ) and SO(n, n; ℤ).

AB - We make a modest progress in the nonuniform measure rigidity program started in 2007 and its applications to the Zimmer program. The principal innovation is in establishing rigidity of large measures for actions of ℤk, k ≥ 2 with pairs of negatively proportional Lyapunov exponents which translates to applicability of our results to actions of lattices in higher rank semisimple Lie groups other than SL(n, ℝ), namely, Sp(2n, ℤ) and SO(n, n; ℤ).

UR - http://www.scopus.com/inward/record.url?scp=85029562292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029562292&partnerID=8YFLogxK

U2 - 10.1090/conm/692/13923

DO - 10.1090/conm/692/13923

M3 - Chapter

AN - SCOPUS:85029562292

T3 - Contemporary Mathematics

SP - 195

EP - 208

BT - Contemporary Mathematics

PB - American Mathematical Society

ER -

^{k}actions of symplectic type. In Contemporary Mathematics. American Mathematical Society. 2017. p. 195-208. (Contemporary Mathematics). https://doi.org/10.1090/conm/692/13923