Mathematics – Dynamical Systems
Scientific paper
2010-06-27
Mathematics
Dynamical Systems
18 pages, changes suggested by the referee incorporated, to appear in Ergodic Theory and Dynamical Systems
Scientific paper
We study the limiting behavior of multiple ergodic averages involving several not necessarily commuting measure preserving transformations. We work on two types of averages, one that uses iterates along combinatorial parallelepipeds, and another that uses iterates along shifted polynomials. We prove pointwise convergence in both cases, thus answering a question of I.Assani in the former case, and extending results of B.Host-B.Kra and A.Leibman in the latter case. Our argument is based on some elementary uniformity estimates of general bounded sequences, decomposition results in ergodic theory, and equidistribution results on nilmanifolds.
Chu Qing
Frantzikinakis Nikos
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