论文标题
pinsker $σ$ -Algebra角色和卑鄙的li-yorke混乱
Pinsker $σ$-algebra Character and mean Li-Yorke chaos
论文作者
论文摘要
令$ g $为无限的可计数委员会。对于任何$ g $ action在紧凑型公制$ x $上的任何$ g $ action，证明，对于任何序列$（g_n）_ {n \ ge 1} $，由$ \ lim_ {n \ to \ lim_ {n \ to \ for \ for \ infty} | g_n | g_n | g_n | g_n | pinskerge $ -pinsker $ -albra组成的$ g $的非空的有限子集组成$（g_n）_ {n \ ge 1} $。结果，对于一类$ g $的动力学系统，积极的拓扑熵意味着沿着一类序列的li-yorke混乱，这些序列由$ g $的非空的有限子集组成。
Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $X$, it is proved that for any sequence $(G_n)_{n\ge 1}$ consisting of non-empty finite subsets of $G$ with $\lim_{n\to \infty}|G_n|=\infty$, Pinsker $σ$-algebra is a characteristic factor for $(G_n)_{n\ge 1}$. As a consequence, for a class of $G$-topological dynamical systems, positive topological entropy implies mean Li-Yorke chaos along a class of sequences consisting of non-empty finite subsets of $G$.
