Non-uniform measure rigidity for ℤk actions of symplectic type

Research output: Chapter in Book/Report/Conference proceedingChapter

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 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).

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages195-208
Number of pages14
DOIs
StatePublished - Jan 1 2017

Publication series

NameContemporary Mathematics
Volume692
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Non-uniform measure rigidity for ℤ<sup>k</sup> actions of symplectic type'. Together they form a unique fingerprint.

  • Cite this

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