7 papers
A Hard-Core Subshift Whose Sofic Mean Dimension Depends on the Sofic Approximation
Xianqiang Li, Zhuowei Liu
We exhibit a topologically mixing continuous-alphabet subshift of the free group whose sofic mean dimension depends on the chosen homomorphic sofic approximation, which gives…
Equivalence of Sofic -Metric Mean Dimensions and a Tame-Metric Variational Formula
Xianqiang Li, Zhuowei Liu
Let be a countable discrete sofic group acting by homeomorphisms on a compact metrizable space and a sofic approximation of . We prove that for every $1\leq p<\in…
Relative entropy, topological pressure and variational principle for locally compact sofic group actions
Xianqiang Li, Zhuowei Liu
For a locally compact sofic group continuously acting on a compact metric space, we first study the relative sofic entropy and prove an additive inequality relating sofic entropy a…
Equivalence between sofic metric mean dimension and sofic -metric mean dimension with a product formula
Xianqiang Li
In this paper, we prove the equivalence between sofic -metric mean dimension and sofic metric mean dimension. This answers a question of Hayes in \cite{HB }. Furthermore, we est…
Sofic conditional mean dimension, relative sofic mean dimension and their localizations
Xianqiang Li, Zhuowei Liu, Xiaofang Luo
Let be a factor map between continuous actions of a sofic group , we study sofic conditional mean dimension and relative sofic mean dimension introduced in…
Mean Hausdorff Dimension of Some Infinite Dimensional Fractals for Amenable Group Actions
Xianqiang Li, Xiaofang Luo
For the countable discrete amenable group actions, we calculate the mean Hausdorff dimensions of three types of infinite dimensional fractal systems, the self-similar systems, homo…