14 citations · 25 across the 16 of their papers we have counts for
16 papers
Topological entropy, mean dimension, and weakly equivalent flows
Lei Jin, Yixiao Qiao
In this paper, we mainly revisit a nice theory for topological entropy of weakly equivalent flows, which was originally investigated by Ohno in 1980. We will develop a new approach…
Infinite topological entropy, positive mean dimension, and factors of subshifts
Lei Jin, Yixiao Qiao
We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' con…
Sofic approximation sequences and sofic mean dimension
Lei Jin, Yixiao Qiao
The main purpose of this paper is to strengthen our understanding of sofic mean dimension of two typical classes of sofic group actions. First, we study finite group actions. We pr…
Mean dimension of Bernstein spaces and universal real flows
Lei Jin, Yixiao Qiao, Siming Tu
We study the action of translation on the spaces of uniformly bounded continuous functions on the real line which are uniformly band-limited in a compact interval. We prove that tw…
Directional mean dimension and continuum-wise expansive -actions
Sebastián Donoso, Lei Jin, Alejandro Maass +1
We study directional mean dimension of -actions (where is a positive integer). On the one hand, we show that there is a -action whose directional me…
Sofic mean dimension of typical actions and a comparison theorem
Lei Jin, Yixiao Qiao
We refine two results in the paper entitled "Sofic mean dimension" by Hanfeng Li, improving two inequalities with two equalities, respectively, for sofic mean dimension of typical…
Mean dimension of product spaces: a fundamental formula
Lei Jin, Yixiao Qiao
Mean dimension is a topological invariant of dynamical systems, which originates with Mikhail Gromov in 1999 and which was studied with deep applications around 2000 by Elon Linden…
The Hilbert cube contains a minimal subshift of full mean dimension
Lei Jin, Yixiao Qiao
We construct a minimal dynamical system of mean dimension equal to , which can be embedded in the shift action on the Hilbert cube . This clarifies a seemingly…
Mean dimension and a non-embeddable example for amenable group actions
Lei Jin, Kyewon Koh Park, Yixiao Qiao
For every infinite (countable discrete) amenable group and every positive integer we construct a minimal -action of mean dimension which cannot be embedded in the…
Zero-dimensional isomorphic dynamical models
Tomasz Downarowicz, Lei Jin, Wolfgang Lusky +1
By an \emph{assignment} we mean a mapping from a Choquet simplex to probability measure-preserving systems, obeying some natural restrictions. We prove that if is an aperio…
A new universal real flow of the Hilbert-cubical type
Lei Jin, Siming Tu
We provide a new universal real flow of the Hilbert-cubical type. We prove that any real flow can be equivariantly embedded in the translation on , where…
A Lipschitz refinement of the Bebutov--Kakutani dynamical embedding theorem
Yonatan Gutman, Lei Jin, Masaki Tsukamoto
We prove that an -action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions if its fixed point set can be topol…
Mean dimension and an embedding theorem for real flows
Yonatan Gutman, Lei Jin
We develop mean dimension theory for -flows. We obtain fundamental properties and examples and prove an embedding theorem: Any real flow of mean dimens…
An explicit compact universal space for real flows
Yonatan Gutman, Lei Jin
The Kakutani-Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of embeds into the Bebutov flow, the $\m…
Mean proximality and mean Li-Yorke chaos
Felipe García-Ramos, Lei Jin
We prove that if a topological dynamical system is mean sensitive and contains a mean proximal pair consisting of a transitive point and a periodic point, then it is mean Li-Yorke…
Stable sets and mean Li-Yorke chaos in positive entropy actions of bi-orderable amenable groups
Wen Huang, Lei Jin
It is proved that positive entropy implies mean Li-Yorke chaos for a G-system, where G is a countable infinite discrete bi-orderable amenable group. Examples are given for the case…