100 citations · 105 across the 9 of their papers we have counts for
10 papers
Relative topological entropy and relative mean dimension of induced factors
Kairan Liu, Yixiao Qiao
We study the relation of relative topological entropy and relative mean dimension between a factor map and its induced factor map for amenable group actions. On the one hand, we pr…
Local entropy theory, combinatorics, and local theory of Banach spaces
Hanfeng Li, Kairan Liu
Each continuous action of a countably infinite discrete group on a compact metrizable space X induces a continuous action of on the space M(X) of Borel probability measures…
Relative uniformly positive entropy of induced amenable group actions
Kairan Liu, Runju Wei
Let be a countable infinite discrete amenable group.It should be noted that a -system naturally induces a -system , where den…
Bernoullicity of lopsided principal algebraic actions
Hanfeng Li, Kairan Liu
We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some orderability condition are Bern…
Mean Li-Yorke chaos along polynomials of several variables and prime numbers
Kairan Liu
In this paper, for any given polynomial, by analyzing the limiting behavior of ergodic averages along polynomials of several variables and prime numbers, we prove that for a topolo…
Time-restricted sensitivity and entropy
Kairan Liu, Leiye Xu, Ruifeng Zhang
In this paper, we consider measure-theoretical restricted sensitivity and topological restricted sensitivities by restricting the first sensitive time. For a given topological dyna…
-weakly mixing subsets along a collection of sequences of integers
Jian Li, Kairan Liu
In this paper, we propose a mild condition, named Condition , for collections of sequence of integers and show that for any measure preserving system the Pinsker -algebra…
Topological entropy of nonautonomous dynamical systems
Kairan Liu, Yixiao Qiao, Leiye Xu
Let be the space of Borel probability measures on a compact metric space endowed with the weak-topology. In this paper, we prove that if the topological…
-Weakly Mixing Subset In Positive Entropy Actions Of A Nilpotent Group
Kairan Liu
The notion of -weakly mixing subsets is introduced for countable torsion-free discrete group actions. It is shown that for a finitely generated torsion-free discrete nilpotent g…
Auslander-Yorkes type dichotomy theorems for stronger version r-sensitivity
Kairan Liu, Xiaomin Zhou
In this paper, for r in N with r>=2 we consider several stronger version r-sensitivities and measure-theoretical r-sensitivities by analysing subsets of nonnegative integers, for w…