Mean Li-Yorke chaos along some good sequences
Mean Li-Yorke chaos along some good sequences
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沿着一些好的序列平均李约克混乱
DOI：
10.1007/s00605-017-1086-2
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发表时间：
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通讯作者：
Yixiao Qiao
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作者：
Jian Li;Yixiao Qiao
如果一个拓扑动力系统(X，T)有正拓扑熵，则它是沿正整数序列的多元平均Li-Yorke混沌的，这对于逐点遍历收敛是“好”的，且条件温和；更具体地说，存在一个Cantor子集KofX，使得对每个两两不同的点Kwe有$Begin{alized}\liminf_{N\right tarrow\inty}\frac{1}{N}\sum_{k=1}^N\max_{1\le i<；J\le n}d\Left(T^{a_k}x_i，T^{a_k}x_j\right)=0\end{alized}$$和$\Begin{alized}\limsup_{N\right tarrow\infty}\frac{1}{N}\sum_{k=1}^N\min_{1\le i<；j\le n}d\Left(T^{a_k}x_i，T^{a_k}x_j\right)>；0。最后给出了经典素数序列和广义多项式序列的例子.
If a topological dynamical system (X,T) has positive topological entropy, then it is multivariant mean Li–Yorke chaotic along a sequenceof positive integers which is “good” for pointwise ergodic convergence with a mild condition; more specifically, there exists a Cantor subsetKofXsuch that for everyand pairwise distinct pointsinKwe have $$\begin{aligned} \liminf _{N\rightarrow \infty }\frac{1}{N}\sum _{k=1}^N\max _{1\le i<j\le n} d\left( T^{a_k}x_i,T^{a_k}x_j\right) =0 \end{aligned}$$and $$\begin{aligned} \limsup _{N\rightarrow \infty }\frac{1}{N}\sum _{k=1}^N\min _{1\le i<j\le n} d\left( T^{a_k}x_i,T^{a_k}x_j\right) >0. \end{aligned}$$Examples are given for the classic sequences of primes and generalized polynomials.