Multiple and Polynomial Recurrence for Abelian Actions in Infinite Measure

@inproceedings{Danilenko2002MultipleAP,
  title={Multiple and Polynomial Recurrence for Abelian Actions in Infinite Measure},
  author={Alexandre I. Danilenko and Cesar E. Silva},
  year={2002}
}
We apply the (C, F )-construction from [Da] to produce a number of funny rank one infinite measure preserving actions of Abelian groups G with “unusual” multiple recurrence properties. In particular, we construct the following for each p ∈ N ∪ {∞}: (i) a p-recurrent action T = (Tg)g∈G such that (if p 6= ∞) no one transformation Tg is (p + 1)-recurrent for… CONTINUE READING