We prove the L2 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.
|Original language||English (US)|
|Number of pages||19|
|Journal||Israel Journal of Mathematics|
|State||Published - 2005|
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