论文标题
正熵意味着沿任何无限序列的混乱
Positive entropy implies chaos along any infinite sequence
论文作者
论文摘要
令$ g $为无限的可计数委员会。对于紧凑型公制空间$（x，ρ）$上的任何$ g $ - 付费，事实证明，如果该动作具有积极的拓扑熵，那么对于任何序列$ \ {s_i \} _ {i = 1}^^}^{+\ \ \ \ \\ infty} $，与$ g $ contoty con $ k $ k $ k x $ x $ x $ x $两个不同的点$ x，y \在k $中，一个具有\ [\ limsup_ {i \ to+\ fo+\ infty}ρ（s_i x，s_iy）> 0，\ \ \ \ text {and} {and}
Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $(X,ρ)$, it turns out that if the action has positive topological entropy, then for any sequence $\{s_i\}_{i=1}^{+\infty}$ with pairwise distinct elements in $G$ there exists a Cantor subset $K$ of $X$ which is Li-Yorke chaotic along this sequence, that is, for any two distinct points $x,y\in K$, one has \[\limsup_{i\to+\infty}ρ(s_i x,s_iy)>0,\ \text{and}\ \liminf_{i\to+\infty}ρ(s_ix,s_iy)=0.\]
