### 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 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Katok, A., & Hertz, F. R. (2017). Non-uniform measure rigidity for ℤ

^{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