On the multiple recurrence properties for disjoint systems

2020/09/22 by Hirayama, Michihiro, Kim, Dong Han, Son, Younghwan
#28D05 #37A05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.10566

Abstract

We consider mutually disjoint family of measure preserving transformations T₁, ⋯, T_k on a probability space (X, B, μ). We obtain the multiple recurrence property of T₁, ⋯, T_k and this result is utilized to derive multiple recurrence of Poincaré type in metric spaces. We also present multiple recurrence property of Khintchine type. Further, we study multiple ergodic averages of disjoint systems and we show that T₁, ⋯, T_k are uniformly jointly ergodic if each T_i is ergodic.

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