2019/11/13 by Qiu, Jiahao, Zhao, Jianjie
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1911.05435
In this paper, it is shown that for d∈ℕ, a minimal system (X,T) is a d-step pro-nilsystem if its enveloping semigroup is a d-step top-nilpotent group, answering an open question by Donoso. Thus, combining the previous result of Donoso, it turns out that a minimal system (X,T) is a d-step pro-nilsystem if and only if its enveloping semigroup is a d-step top-nilpotent group.