Distinguishing sets of strong recurrence from van der Corput Sets

2022/03/25 by Andreas Mountakis, Mountakis, Andreas
Biochemistry, Genetics and Molecular Biology · Computer Science · #37A46 #Algorithms and Data Compression #Dynamical Systems (math.DS) #FOS: Mathematics #RNA Research and Splicing

paper · pdf · doi:10.48550/arxiv.2203.13804

openalex publication_date 2022/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a set of strong recurrence which is not a van der Corput set. This shows that the class of enhanced van der Corput sets is a proper subclass of sets of strong recurrence. In addition, we derive that the class of sets of strong recurrence is not a subclass of van der Corput sets. This answers some questions asked by Bergelson and Lesigne.

Related

• Van der Corput sets in Z^d
• An inverse of Furstenberg's correspondence principle and applications to van der Corput sets
• Asymptotic dynamics on amenable groups and van der Corput sets
• On Alweiss's example for multiple recurrence
• On Recurrence Axioms