Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 13
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    BERGELSON, VITALY and ROBERTSON, DONALD 2016. Polynomial multiple recurrence over rings of integers. Ergodic Theory and Dynamical Systems, Vol. 36, Issue. 05, p. 1354.


    FRANTZIKINAKIS, NIKOS and HOST, BERNARD 2016. Weighted multiple ergodic averages and correlation sequences. Ergodic Theory and Dynamical Systems, p. 1.


    Austin, Tim 2015. Pleasant extensions retaining algebraic structure, II. Journal d'Analyse Mathématique, Vol. 126, Issue. 1, p. 1.


    FRANTZIKINAKIS, NIKOS and ZORIN-KRANICH, PAVEL 2015. Multiple recurrence for non-commuting transformations along rationally independent polynomials. Ergodic Theory and Dynamical Systems, Vol. 35, Issue. 02, p. 403.


    LEIBMAN, A. 2015. Nilsequences, null-sequences, and multiple correlation sequences. Ergodic Theory and Dynamical Systems, Vol. 35, Issue. 01, p. 176.


    BERGELSON, V. LEIBMAN, A. and MOREIRA, C. G. 2012. From discrete- to continuous-time ergodic theorems. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 02, p. 383.


    CHU, QING and FRANTZIKINAKIS, NIKOS 2012. Pointwise convergence for cubic and polynomial multiple ergodic averages of non-commuting transformations. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 03, p. 877.


    Green, Ben and Tao, Terence 2012. The quantitative behaviour of polynomial orbits on nilmanifolds. Annals of Mathematics, Vol. 175, Issue. 2, p. 465.


    Leibman, A. 2012. A canonical form and the distribution of values of generalized polynomials. Israel Journal of Mathematics, Vol. 188, Issue. 1, p. 131.


    LEIBMAN, A. 2010. Multiple polynomial correlation sequences and nilsequences. Ergodic Theory and Dynamical Systems, Vol. 30, Issue. 03, p. 841.


    Bergelson, V. Leibman, A. and Lesigne, E. 2008. Intersective polynomials and the polynomial Szemerédi theorem. Advances in Mathematics, Vol. 219, Issue. 1, p. 369.


    BURGIN, MARK and DUMAN, OKTAY 2008. STATISTICAL FUZZY CONVERGENCE. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 16, Issue. 06, p. 879.


    Bergelson, Vitaly and Leibman, Alexander 2007. Distribution of values of bounded generalized polynomials. Acta Mathematica, Vol. 198, Issue. 2, p. 155.


    ×
  • Ergodic Theory and Dynamical Systems, Volume 25, Issue 1
  • February 2005, pp. 215-225

Pointwise convergence of ergodic averages for polynomial actions of $\mathbb{Z}^{d}$ by translations on a nilmanifold

  • A. LEIBMAN (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385704000227
  • Published online: 22 December 2004
Abstract

Generalizing the one-parameter case, we prove that the orbit of a point on a compact nilmanifold X under a polynomial action of $\mathbb{Z}^{d}$ by translations on X is uniformly distributed on the union of several sub-nilmanifolds of X. As a corollary we obtain the pointwise ergodic theorem for polynomial actions of $\mathbb{Z}^{d}$ by translations on a nilmanifold.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax