Li–Yorke chaos · Jiayu Chen

Li-Yorke混沌

Dynamical Systems · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A continuous map of a metric space is Li–Yorke chaotic when it admits an uncountable set in which every distinct pair satisfies $\liminf_n d(T^nx,T^ny)=0$ and $\limsup_n d(T^nx,T^ny)>0$ .

存在不可数点集，其中任意不同两点的迭代距离下极限为0且上极限为正的连续系统性质。

Example

The full binary shift admits such a set by interleaving shared zero blocks with repeatedly separated coded blocks.

Usage and distinctions

One scrambled pair is not an uncountable scrambled set; a common positive limsup bound is an additional uniform variant.

Definition sources

李健、谭枫 — 关于 Li-Yorke δ-混沌与按序列分布 δ-混沌的等价性Printed p.34, Definition 1, scrambled-pair equations and uncountable-set condition · Checked 2026-10-14

Translation sources

李健、谭枫 — 关于 Li-Yorke δ-混沌与按序列分布 δ-混沌的等价性Printed p.34，定义1：Li-Yorke混沌 · Checked 2026-10-14

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