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引用次数: 0
摘要
让 G 是一个无限可数离散可亲群。对于紧凑度量空间X上的任意G作用,证明了对于由G的非空有限子集组成的任意序列\((G_n)_{n\rightarrow \infty }|G_n|=\infty \),平斯克(Pinsker)(\sigma \)代数是\((G_n)_{n\ge 1}\)的特征因子。因此,对于一类 G 拓扑动力系统,正拓扑熵意味着沿着一类由 G 的非空有限子集组成的序列的平均李-约克混沌。
Pinsker $$\sigma $$ -Algebra Character and Mean Li–Yorke Chaos
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 \(\lim _{n\rightarrow \infty }|G_n|=\infty \), Pinsker \(\sigma \)-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.
期刊介绍:
Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.