Relative entropy dimensions for amenable group actions

2022/01/10 by Zubiao Xiao, Zhengyu Yin, Xiao, Zubiao +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2201.03150

Abstract

We study the topological complexities of relative entropy zero extensions acted by countableinfinite amenable groups. Firstly, for a given Folner sequence \F_n\_n=0^∞, we define respectively the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity. Meanwhile, we investigate the relations among them. Secondly, we introduce the notion of a relative dimension set. Moreover, using it, we discuss the disjointness between the relative entropy zero extensions which generalizes the results of Dou, Huang and Park[Trans. Amer. Math. Soc. 363(2) (2011), 659-680].

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