Seminorms for multiple averages along polynomials and applications to joint ergodicity
2021; Springer Science+Business Media; Volume: 146; Issue: 1 Linguagem: Inglês
10.1007/s11854-021-0186-z
ISSN1565-8538
AutoresSebastián Donoso, Andreas Koutsogiannis, Wenbo Sun,
Tópico(s)Advanced Topology and Set Theory
ResumoExploiting the recent work of Tao and Ziegler on the concatenation theorem on factors, we find explicit characteristic factors for multiple averages along polynomials on systems with commuting transformations, and use them to study criteria of joint ergodicity for sequences of the form $$(T_{1}^{p_{1,j}(n)}\cdots T_{d}^{p_{d,j}(n)})_{n\in\mathbb{Z}}$$ , 1 ≤ j ≤ k, where T1, …, Td are commuting measure preserving transformations on a probability measure space and pi, j are integer polynomials. To be more precise, we provide a sufficient condition for such sequences to be jointly ergodic, giving also a characterization for sequences of the form $$(T_{i}^{p(n)})_{n\in\mathbb{Z}}$$ , 1 ≤ i ≤ d to be jointly ergodic, answering a question due to Bergelson.
Referência(s)