Multiple recurrence for two commuting transformations

By Q. Chu. Ergodic Theory and Dynamical Systems, 2009

52 citations recorded by the source corpus.

Abstract This paper is devoted to a study of the multiple recurrence of two commuting transformations. We derive a result which is similar but not identical to that established by Bergelson, Host and Kra for one single transformation. We use the machinery of ‘magic systems’ established recently by B. Host for the proof.

Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/76eeb5c6e4a134cf7e5a7b4fad1eee53d4f64a6b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Q. Chu
2. Nikos Frantzikinakis
3. B. Host
4. Terence Tao
5. T. Ziegler
6. Bryna Kra
7. M. N. Walsh
8. Tim Austin

In Electrical and Electronic Engineering

1. Nikos Frantzikinakis
2. B. Host

In Mathematical Physics

1. Q. Chu
2. Nikos Frantzikinakis
3. B. Host
4. Terence Tao
5. T. Ziegler
6. M. N. Walsh
7. Bryna Kra
8. Ben Joseph Green

Citations in the corpus

• Some open problems on multiple ergodic averages (2011, background): “lent places to look for such topics, for instance, the survey articles of V. Bergelson [24, 27, 28] cover a lot of related material and contain an extensive bibliography up to 2006. Linear sequences: [2, 3, 5, 6, 7, 9, 10, 14, 15, 16, 17, 18, 25, 56, 33, 36, 37, 59, 60, 63, 64, 65, 68, 69, 73, 75, 7”
• Ergodic averages of commuting transformations with distinct degree polynomial iterates (2009, background): “If = 2, d1 = d2 = 1, and the joint action of the transformations T1, T2 is ergodic, then the result remains true up to a change of the exponent on the right-hand side [10].”