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math.DS2022
Application of waist inequality to entropy and mean dimension
Ruxi Shi, Masaki Tsukamoto
Waist inequality is a fundamental inequality in geometry and topology. We apply it to the study of entropy and mean dimension of dynamical systems. We consider equivariant continuo…
math.DS2022★ 2 cited
Mean Hausdorff dimension of some infinite dimensional fractals
Masaki Tsukamoto
Mean Hausdorff dimension is a dynamical version of Hausdorff dimension. It provides a way to dynamicalize geometric measure theory. We pick up the following three classical results…
math.DS2022
On an analogue of the Hurewicz theorem for mean dimension
Masaki Tsukamoto
The Hurewicz theorem is a fundamental result in classical dimension theory concerning continuous maps which lower topological dimension. We study whether or not its analogue holds…