关于Li-Yorke Δ-混沌与按序列分布Δ-混沌的等价性
THE EQUIVALENCE RELATIONSHIP BETWEEN LI-YORKE Δ-CHAOS AND DISTRIBUTIONAL Δ-CHAOS IN A SEQUENCE
-
摘要: 关注~Li-Yorke~混沌和按序列分布混沌的关系, 指出全体按序列~Q~分布~\delta-攀援偶对构成的集合为乘积空间中的一个~G_\delta~集.证明了: (1)~Li-Yorke~\delta-混沌等价于按序列分布~\delta-混沌; (2)~一致混乱集是按某序列分布攀援集; (3)~一类传递系统蕴含了按序列分布混沌.Abstract: The relationship between Li-Yorke chaos and distributional chaos in a sequence is discussed. It is pointed out that the set of distributional \delta-scramble pairs in a sequence Q is a G_\delta set, and Li-Yorke \delta-chaos is equivalent to distributional \delta-chaos in a sequence. A uniformly chaotic set is a distributional scramble set in some sequence and a class of transitive system implies distributional chaos in a sequence.