29 citations · 106 across the 33 of their papers we have counts for
34 papers
Simple proof of the global inverse function theorem via the Hopf--Rinow theorem
Shinobu Ohkita, Masaki Tsukamoto
We explain that Hadamard's global inverse function theorem very simply follows from the Hopf--Rinow theorem in Riemannian geometry.
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…
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…
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…
New approach to weighted topological entropy and pressure
Masaki Tsukamoto
Motivated by fractal geometry of self-affine carpets and sponges, Feng--Huang (2016) introduced weighted topological entropy and pressure for factor maps between dynamical systems,…
Divergent coindex sequence for dynamical systems
Ruxi Shi, Masaki Tsukamoto
When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between t…