topological mixing

拓扑混合

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

Other names / variants: topological strong mixing

Translation evidence: Literature usage

Meaning in context

A continuous self-map $T$ is topologically mixing when for every nonempty open $U,V$, some $N$ makes $T^n(U)\cap V\ne\varnothing$ for every $n\ge N$.

任意两个非空开区域在所有充分大的迭代时刻均能相连的连续动力系统性质。

Example

The one-sided full binary shift is topologically mixing by concatenating prescribed words with any sufficiently long gap.

Usage and distinctions

It requires every sufficiently late time, not just one time; it says nothing about event probabilities for a chosen measure.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. 陈绥阳、褚蕾蕾 — 动力系统基础及其方法（科学出版社预览）§2.3，定义2.3.2，p.17，所有充分大n的开集相交条件 · Checked 2026-10-14

Translation sources

1. 陈绥阳、褚蕾蕾 — 动力系统基础及其方法（科学出版社预览）§2.3，定义2.3.2，p.17：拓扑混合的 · Checked 2026-10-14

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