An extension of Furstenberg's structure theorem for Noetherian modules and multiple recurrence theorems III

Abstract

Using a recent Furstenberg structure theorem, we obtain Multiple Recurrence Theorems relative to any locally compact second countable Noetherian module $G$ over a syndetic ring $R$, which generalizes Furstenberg's multiple recurrence theorem. In addition we study the multiple Birkhoff center and the pointwise multiple recurrence of a topological $G$-action on a compact metric space.

22 pages

References in corpus (2)

• Multi-recurrence and van der Waerden systems
• Grünwald version of van der Waerden's theorem for semi-modules