Relative entropy dimensions for amenable group actions
Dynamical Systems
2022-01-11 v1
Abstract
We study the topological complexities of relative entropy zero extensions acted by countableinfinite amenable groups. Firstly, for a given Folner sequence , 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].
Cite
@article{arxiv.2201.03150,
title = {Relative entropy dimensions for amenable group actions},
author = {Zubiao Xiao and Zhengyu Yin},
journal= {arXiv preprint arXiv:2201.03150},
year = {2022}
}