Israel Journal of Mathematics

, Volume 149, Issue 1, pp 1–19

Convergence of polynomial ergodic averages


    • Équipe d’analyse et de mathématiques appliquéesUniversité de Marne la Vallée
  • Bryna Kra
    • Department of Mathematics, McAllister B uildingThe Pennsylvania State University

DOI: 10.1007/BF02772534

Cite this article as:
Host, B. & Kra, B. Isr. J. Math. (2005) 149: 1. doi:10.1007/BF02772534


We prove theL2 convergence for an ergodic average of a product of functions evaluated along polynomial times in a totally ergodic system. For each set of polynomials, we show that there is a particular factor, which is an inverse limit of nilsystems, that controls the limit behavior of the average. For a general system, we prove the convergence for certain families of polynomials.

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© Hebrew University 2005