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math.DS2025
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…
math.DS2024
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…
math.DS2024
Amenable Metric Mean Dimension and Amenable Mean Hausdorff Dimension of Product Sets and Metric Varying
Xianqiang Li, Xiaofang Luo
Metric mean dimension and mean Hausdorff dimension depend on metrics. In this paper, we investigate the continuity of the metric mean dimension and mean Hausdorff dimension concern…