TY - JOUR
T1 - On the multiple recurrence properties for disjoint systems
AU - Hirayama, Michihiro
AU - Kim, Dong Han
AU - Son, Younghwan
N1 - Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.
PY - 2022/4
Y1 - 2022/4
N2 - We consider a mutually disjoint family of measure preserving transformations T1, …, Tk on a probability space (Xℬμ). We obtain the multiple recurrence property of T1, …, Tk and this result is utilized to derive multiple recurrence of Poincaré type in metric spaces. We also present the multiple recurrence property of Khintchine type. Further, we study multiple ergodic averages of disjoint systems and we show that T1, …, Tk are uniformly jointly ergodic if each Ti is ergodic.
AB - We consider a mutually disjoint family of measure preserving transformations T1, …, Tk on a probability space (Xℬμ). We obtain the multiple recurrence property of T1, …, Tk and this result is utilized to derive multiple recurrence of Poincaré type in metric spaces. We also present the multiple recurrence property of Khintchine type. Further, we study multiple ergodic averages of disjoint systems and we show that T1, …, Tk are uniformly jointly ergodic if each Ti is ergodic.
UR - http://www.scopus.com/inward/record.url?scp=85121663495&partnerID=8YFLogxK
U2 - 10.1007/s11856-021-2271-5
DO - 10.1007/s11856-021-2271-5
M3 - Article
AN - SCOPUS:85121663495
SN - 0021-2172
VL - 247
SP - 405
EP - 431
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -