Chaos on the Multi-Dimensional Cube

Li-Yorke sensitivity does not imply Li-Yorke chaos

We construct an infinite-dimensional compact metric space $X$, which is a closed subset of $\mathbb{S}\times\mathbb{H}$, where $\mathbb{S}$ is the unit circle and $\mathbb{H}$ is the Hilbert cube, and a skew-product map $F$ acting on $X$ such that $(X,F)$ is Li-Yorke sensitive but possesses at most countable scrambled sets. This disproves the conjecture of Akin and Kolyada that Li-Yorke sensitivity implies Li-Yorke chaos from the article [Akin E., Kolyada S., Li-Yorke sensitivity, Nonlinearity 16, (2003), 1421-1433].

Hetero-dimensional baker maps and Dyck shifts

We give piecewise affine maps on the unit cube whose symbolic representation is the Dyck shift. This leads to a different way of verifying the chaotic nature of this system, including the computation of entropy.

乘法立方体与乘法自动机

Multiplication cubes and multiplication automata

该研究将二维pq进制下模拟p、q乘法的乘法铺砌系统推广到高维乘法镶嵌系统，构建相关理论并通过宏块操作关联不同系统，进而得到不同进制乘法元胞自动机间的拓扑共轭与因子映射。

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

In this paper, we study various chaos of topological group or semigroup actions.

多重映射的混合性、Li-Yorke混沌、分布混沌与Kato混沌

Mixing, Li-Yorke chaos, distributional chaos and Kato's chaos to multiple mappings

本文从集值视角定义多重映射的传递性与混合性等概念，证明多重映射的混合性蕴含三类混沌，给出Kato混沌的迭代等价性，并构造符号动力系统验证仅两个强非游荡点即可产生分布混沌。

Multi-chaos from Quasiperiodicity

One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to characterize such systems we define a property called "multi-chaos". A set $X$ is multi-chaotic if $X$ has a dense trajectory and for at least 2 values of $k$, the $k$-dimensionally unstable periodic points are dense in $X$. All proofs that such a behavior holds have been based on hyperbolicity in the sense that (i) there is a chaotic set $X$ with a dense trajectory…