Convergence of polynomial ergodic averages
- Cite this article as:
- Host, B. & Kra, B. Isr. J. Math. (2005) 149: 1. doi:10.1007/BF02772534
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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.