Ergodic Theory and Dynamical Systems

Research Article

Cube spaces and the multiple term return times theorem


Korteweg-de Vries Institute for Mathematics, University of Amsterdam, PO Box 94248, 1090 GE Amsterdam, The Netherlands email


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.

(Received October 20 2012)

(Revised January 11 2013)