21 citations · 43 across the 29 of their papers we have counts for
4 papers · 1 filter
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…
Topological mean dimension of induced systems
David Burguet, Ruxi Shi
For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak- topology has infini…
Strongly isomorphic symbolic extensions for expansive topological flows
Yonatan Gutman, Ruxi Shi
In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This…
Mean dimension of natural extension of algebraic systems
Bingbing Liang, Ruxi Shi
Mean dimension may decrease after taking the natural extension. In this paper we show that mean dimension is preserved by natural extension for an endomorphism on a compact metriza…