4 papers
A Lipschitz refinement of the Bebutov-Kakutani dynamical embedding theorem for connected Lie group actions
Yonatan Gutman, Qiang Huo, Kangbo Ouyang
Let be a connected Lie group equipped with a compatible right-invariant metric and let act continuously on a compact metrizable space . We prove that admits a -eq…
Mean Assouad dimension and spectrum, with applications to infinite dimensional fractals
Qiang Huo, Adam Śpiewak
We introduce the mean Assouad dimension of a dynamical system, motivated by the Assouad dimension in fractal geometry. Using dimension interpolation, we further define the mean Ass…
A Lipschitz Refinement of the Multidimensional Bebutov--Kakutani Dynamical Embedding Theorem
Yonatan Gutman, Qiang Huo, Masaki Tsukamoto
We prove that a continuous action of on a compact metrizable space equivariantly embeds into the shift action on the space of one-Lipschitz functions from $\mathbb{R…
On the representation of measurable and continuous dynamical systems by Lipschitz functions
Yonatan Gutman, Qiang Huo
Two representations theorems are presented: 1. Any Borel action of a second countable locally compact group on a standard Borel space admits an injective -equivariant Bo…