Article

Israel Journal of Mathematics

, Volume 149, Issue 1, pp 1-19

Convergence of polynomial ergodic averages

  • Bernard HostAffiliated withÉquipe d’analyse et de mathématiques appliquées, Université de Marne la Vallée Email author 
  • , Bryna KraAffiliated withDepartment of Mathematics, McAllister B uilding, The Pennsylvania State University

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Abstract

We prove theL 2 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.