omega-limit set

ω极限点集

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

Other names / variants: omega limit set

Translation evidence: Literature usage

Meaning in context

For a continuous map $T$ on a metric space, $\omega(x)$ is the set of limits of $T^{n_k}x$ along sequences $n_k\to\infty$.

连续映射下一点的正向迭代，沿趋于无穷的时间子序列所得的全部极限点。

Example

For $T(x)=x/2$ on $[0,1]$, $\omega(1)=\{0\}$.

Usage and distinctions

It can differ from the orbit closure, which includes early visited points; compactness ensures nonemptiness.

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2.2.2及注2.2.1，p.13，子序列公式 · 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2.2.2，p.13：ω极限点集 · Checked 2026-10-14

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