topological conjugacy

拓扑共轭

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Translation evidence: Literature usage

Meaning in context

Maps T:X→XT:X\to X and S:Y→YS:Y\to Y are topologically conjugate if a homeomorphism h:X→Yh:X\to Y satisfies h∘T=S∘hh\circ T=S\circ h.

两个系统由一个同胚联系，且先演化再换坐标与先换坐标再演化所得结果相同。

Example

On [0,1][0,1], h(x)=1−xh(x)=1-x conjugates T(x)=x2T(x)=x^2 to S(y)=2y−y2S(y)=2y-y^2.

Usage and distinctions

The conjugacy must be a homeomorphism; a noninvertible intertwining map is a semiconjugacy, and time changes define a different flow equivalence.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gerald Teschl — Ordinary Differential Equations and Dynamical Systems§11.3, equation (11.10) and equivalence discussion · 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）§2.1，定义2.1.4，p.12：拓扑共轭 · Checked 2026-10-14
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