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math.DS2025
Metric mean dimension and the variational principle for actions of amenable groups
Rui Yang, Xiaoyao Zhou
Metric mean dimension is a dynamical counterpart of the box dimension in fractal geometry to characterize the topological complexity of infinite entropy systems. The classical vari…
math.DS2025
Mean dimension and rate-distortion function revisited
Rui Yang
Around the mean dimensions and rate-distortion functions, using some tools from local entropy theory this paper establishes the following main results: We prove that for non-…
math.DS2024
On the metric mean dimensions of saturated sets
Yong Ji, Junye Li, Rui Yang
From a geometric perspective, we employ metric mean dimension to investigate the set of generic points of invariant measures and saturated sets in infinite entropy systems. For sys…