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Cube spaces and the multiple term return times theorem. (English) Zbl 1351.37024

Summary: We give a new proof of Rudolph’s multiple term return times theorem based on Host-Kra structure theory. Our approach provides characteristic factors for all terms, works for arbitrary tempered Følner sequences and also yields a multiple term Wiener-Wintner-type return times theorem for nilsequences.

MSC:

37A25 Ergodicity, mixing, rates of mixing
37A30 Ergodic theorems, spectral theory, Markov operators
37B20 Notions of recurrence and recurrent behavior in topological dynamical systems
28D05 Measure-preserving transformations
37A05 Dynamical aspects of measure-preserving transformations
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