Li–Yorke scrambled pair

Li-Yorke攀援偶对

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

Other names / variants: scrambled pair

Translation evidence: Literature usage

Meaning in context

Distinct points $x,y$ in a metric dynamical system with $\liminf_n d(T^nx,T^ny)=0$ and $\limsup_n d(T^nx,T^ny)>0$.

两个不同点的正迭代距离能任意接近0，却不能最终一直趋于0的偶对。

Example

In the binary shift, compare the all-zero sequence with one whose isolated ones are separated by increasingly long zero blocks.

Usage and distinctions

A proximal pair satisfies only the liminf-zero condition; an asymptotic pair has distance tending to zero and is not scrambled.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. 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, two distance conditions · Checked 2026-10-14

Translation sources

1. 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攀援偶对 · Checked 2026-10-14

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