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

Fingerprint

Rigidity
Semisimple Lie Group
Lyapunov Exponent
Directly proportional
Innovation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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
Katok, Anatole ; Hertz, Federico Rodriguez. / Non-uniform measure rigidity for ℤk actions of symplectic type. Contemporary Mathematics. American Mathematical Society, 2017. pp. 195-208 (Contemporary Mathematics).
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Katok, A & Hertz, FR 2017, Non-uniform measure rigidity for ℤk 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 ℤk actions of symplectic type. / Katok, Anatole; Hertz, Federico Rodriguez.

Contemporary Mathematics. American Mathematical Society, 2017. p. 195-208 (Contemporary Mathematics; Vol. 692).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Katok A, Hertz FR. Non-uniform measure rigidity for ℤk actions of symplectic type. In Contemporary Mathematics. American Mathematical Society. 2017. p. 195-208. (Contemporary Mathematics). https://doi.org/10.1090/conm/692/13923