30 citations · 113 across the 23 of their papers we have counts for
24 papers · 1 filter
Dimensional entropy of amenable group actions over stable sets and fibres
Xinyao He, Guohua Zhang
This paper is devoted to the study of Bowen's dimensional entropy on subsets for actions of amenable groups. We prove three main results. (1) First, topological conditional entropy…
Metric mean dimension of amenable group actions: localization and non-uniformity
Xinyao He, Guohua Zhang, Ruifeng Zhang
In this paper, we extend Tsukamoto's recent localization formula for metric mean dimension to actions of countable discrete amenable groups, which previously applied only to $\math…
Mean topological dimension of induced amenable group actions
Ruxi Shi, Guohua Zhang
In this paper we generalize [BS22, Main Theorem] from actions of a single transformation to amenable group actions, which answers affirmatively the question raised in [BS22] by Bur…
Tail variational principle and asymptotic -expansiveness for amenable group actions
Tomasz Downarowicz, Guohua Zhang
In this paper we prove the tail variational principle for actions of countable amenable groups. This allows us to extend some characterizations of asymptotic -expansiveness from…
Multiorders in amenable group actions
Tomasz Downarowicz, Piotr Oprocha, Mateusz Więcek +1
The paper offers a thorough study of multiorders and their applications to measure-preserving actions of countable amenable groups. By a~{\em multiorder} on a~countable group we me…
The Symbolic Extension Theory in Topological Dynamics
Tomasz Downarowicz, Guohua Zhang
In this survey we will present the symbolic extension theory in topological dynamics, which was built over the past twenty years.
Discrete spectrum for amenable group actions
Tao Yu, Guohua Zhang, Ruifeng Zhang
In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only i…
Symbolic extensions of amenable group actions and the comparison property
Tomasz Downarowicz, Guohua Zhang
Symbolic Extension Entropy Theorem (SEET) describes the possibility of a lossless digitalization of a dynamical system by extending it to a subshift. It gives an estimate on the en…
Quasi-graphs, zero entropy and measures with discrete spectrum
Jian Li, Piotr Oprocha, Guohua Zhang
In this paper, we study dynamics of maps on quasi-graphs characterizing their invariant measures. In particular, we prove that every invariant measure of quasi-graph map with zero…
The comparison property of amenable groups
Tomasz Downarowicz, Guohua Zhang
Let a countable amenable group act on a \zd\ compact metric space . For two clopen subsets and of we say that is \emph{subequivalent}…
Möbius disjointness for topological models of ergodic systems with discrete spectrum
Wen Huang, Zhiren Wang, Guohua Zhang
We provide a criterion for a point satisfying the required disjointness condition in Sarnak's Möbius Disjointness Conjecture. As a direct application, we have that the conjecture h…
Finite intersection property and dynamical compactness
Wen Huang, Danylo Khilko, Sergiy Kolyada +2
Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in [22]. In this paper we continue to investigate t…
Analogues of Auslander-Yorke theorems for multi-sensitivity
Wen Huang, Sergii Kolyada, Guohua Zhang
In this paper we study multi-sensitivity and thick sensitivity for continuous surjective selfmaps on compact metric spaces. We show that multi-sensitivity implies thick sensitivity…
Dynamical compactness and sensitivity
Wen Huang, Danylo Khilko, Sergii Kolyada +1
To link the Auslander point dynamics property with topological transitivity, in this paper we introduce dynamically compact systems as a new concept of a chaotic dynamical system $…
Auslander-Yorke dichotomy theorem, multi-sensitivity and Lyapunov numbers
Wen Huang, Sergii Kolyada, Guohua Zhang
In this paper we study several stronger forms of sensitivity for continuous surjective selfmaps on compact metric spaces and relations between them. The main result of the paper st…
Chaotic behavior of group actions
Zhaolong Wang, Guohua Zhang
In this paper we study chaotic behavior of actions of a countable discrete group acting on a compact metric space by self-homeomorphisms. For actions of a countable discrete group…
Weak expansiveness for actions of sofic groups
Nhan-Phu Chung, Guo Hua Zhang
In this paper, we shall introduce -expansiveness and asymptotical -expansiveness for actions of sofic groups. By the definitions, each -expansive action of sofic groups is…
Sub-additive ergodic theorems for countable amenable groups
Anthony H. Dooley, Valentyn Ya. Golodets, Guohua Zhang
In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.
Lowering topological entropy over subsets revisited
Wen Huang, Xiangdong Ye, Guohua Zhang
Let be a topological dynamical system. Denote by and the covering entropy and dimensional entropy of , respectively. is call…
On weak product recurrence and synchronization of return times
Piotr Oprocha, Guo Hua Zhang
The paper is devoted to study of product recurrence. First, we prove that notions of $\F_{ps}-PR$ and $\F_{pubd}-PR$ are exactly the same as product recurrence, completing that way…
Local variational principle concerning entropy of a sofic group action
Guo Hua Zhang
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with finite entropy; and th…
Local Entropy Theory of a Random Dynamical System
Anthony H. Dooley, Guohua Zhang
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of or is replaced by the action of an infinite countable…
Local entropy theory for a countable discrete amenable group action
Wen Huang, Xiangdong Ye, Guohua Zhang
In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy t…
Lowering topological entropy over subsets
Wen Huang, Xiangdong Ye, Guohua Zhang
Let be a topological dynamical system (TDS), and the topological entropy of a subset of . is {\it lowerable} if for each th…