nonwandering point

非游荡点

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

Translation evidence: Literature usage

Meaning in context

For a continuous self-map $T$, a point $x$ such that every neighborhood $U$ of $x$ has $T^n(U)\cap U\ne\varnothing$ for some integer $n\ge1$.

连续自映射下一点的每个邻域都在某次正迭代后与自身相交。

Example

Every periodic point is nonwandering; every point of the full binary shift is nonwandering.

Usage and distinctions

A returning neighborhood may contain a returning point different from x; nonwandering is weaker than recurrence of x itself.

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）§2.2，定义2.2.4及注2.2.2，pp.14–15，邻域原像公式 · 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）§2.2，定义2.2.4，p.14：非游荡点 · Checked 2026-10-14

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