fixed point in dynamics

不动点

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

Translation evidence: Literature usage

Meaning in context

For a map T:X→XT:X\to X, a point xx with T(x)=xT(x)=x; for a flow, a point fixed by every time map.

离散映射下作用一次仍为自身的点；对流则要求所有时间映射都固定该点。

Example

The map T(x)=x/2T(x)=x/2 has the fixed point 00.

Usage and distinctions

Being fixed by one sampled time map of a flow need not mean equilibrium; a periodic flow orbit may return at that sampling time.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gerald Teschl — Ordinary Differential Equations and Dynamical Systems§6.3 Orbits and invariant sets; §10.2 Fixed and periodic points · 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2.2.1，p.13：周期为1时为不动点 · Checked 2026-10-14
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