flow

流

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

Other names / variants: continuous-time dynamical system

Translation evidence: Literature usage

Meaning in context

A jointly continuous action $\phi:\mathbb R\times X\to X$ with $\phi_0=\operatorname{id}$ and $\phi_{t+s}=\phi_t\circ\phi_s$.

满足零时刻恒同及时间相加对应映射复合的、实数时间对空间的连续作用。

Example

The global solution flow of $\dot x=-x$ is $\phi_t(x)=e^{-t}x$.

Usage and distinctions

All real times are required here; local solutions may explode, and a forward-only semiflow is a different convention.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Gerald Teschl — Ordinary Differential Equations and Dynamical Systems§§6.1–6.2, real-time action and autonomous-equation flow · 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 拓扑动力系统，p.10：G=R时称为流 · Checked 2026-10-14

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