invariant set in topological dynamics

不变集

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

Translation evidence: Literature usage

Meaning in context

For a self-map $T$, a subset $A$ satisfying $T(A)=A$; this record uses equality rather than only forward inclusion.

自映射把该集合的像恰好变为该集合自身的子集；这里采用像相等的约定。

Example

For $T(x)=x^2$ on $[0,1]$, both $\{0\}$ and $[0,1]$ are invariant sets.

Usage and distinctions

Forward invariance $T(A)subseteq A$ is weaker for a general map; measurable invariant events in ergodic theory instead use preimages modulo null sets.

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2.2.3，p.14，f(E)=E · 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2.2.3，p.14：不变集 · Checked 2026-10-14

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