Systems lacking higher order nilfactors

Details Systems lacking higher order nilfactors Systems lacking higher order nilfactors

2012-03-16

arxiv.org/abs/1203.3778v1

Mathematics

Dynamical Systems

Scientific paper

Nilsystems are a natural generalization of rotations and arise in various contexts, including in the study of multiple ergodic averages in ergodic theory, in the structural analysis of topological dynamical systems, and in asymptotics for patterns in certain subsets of the integers. We show, however, that many nat- ural classes of systems in both measure preserving systems and topological dynamical systems contain no higher order nilsystems as factors, meaning that the only nilsystems they contain as fac- tors are rotations. We deduce several ergodic applications of these results.

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