Zorin-Kranich, Pavel Cube spaces and the multiple term return times theorem. (English) Zbl 1351.37024 Ergodic Theory Dyn. Syst. 34, No. 5, 1747-1760 (2014). 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. Cited in 3 Documents 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 Keywords:convergence of averages; measure-preserving map; return times PDFBibTeX XMLCite \textit{P. Zorin-Kranich}, Ergodic Theory Dyn. Syst. 34, No. 5, 1747--1760 (2014; Zbl 1351.37024) Full Text: DOI arXiv References: [1] DOI: 10.1007/BF02698839 · doi:10.1007/BF02698839 [2] DOI: 10.1017/S0143385711000769 · Zbl 1266.37004 · doi:10.1017/S0143385711000769 [3] DOI: 10.1007/BF02762090 · Zbl 0843.28007 · doi:10.1007/BF02762090 [4] Invent. Math. 131 pp 199– (1998) [5] Ergodic Theory and its Connections with Harmonic Analysis (Alexandria, 1993) pp 369– (1995) [6] DOI: 10.1007/BF02764805 · Zbl 0802.28014 · doi:10.1007/BF02764805 [7] DOI: 10.1073/pnas.17.12.656 · Zbl 0003.25602 · doi:10.1073/pnas.17.12.656 [8] DOI: 10.1007/s002220100162 · Zbl 1038.37004 · doi:10.1007/s002220100162 [9] DOI: 10.1017/S0143385704000215 · Zbl 1080.37003 · doi:10.1017/S0143385704000215 [10] DOI: 10.1016/j.aim.2009.11.009 · Zbl 1203.37022 · doi:10.1016/j.aim.2009.11.009 [11] DOI: 10.1007/s11854-009-0024-1 · Zbl 1183.37011 · doi:10.1007/s11854-009-0024-1 [12] DOI: 10.4007/annals.2005.161.397 · Zbl 1077.37002 · doi:10.4007/annals.2005.161.397 [13] Izv. Akad. Nauk. SSSR. Ser. Mat. 13 pp 9– (1949) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.