关于Li-Yorke Δ-混沌与按序列分布Δ-混沌的等价性

详细信息

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.
- Li-Yorke 混沌 /
- 按序列分布混沌 /
- 传递系统
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.
- Li-Yorke chaos /
- distributional chaos in a sequence /
- transitive system