semiflow

半动力系统

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

Other names / variants: continuous-time semidynamical system

Translation evidence: Literature usage

Meaning in context

A jointly continuous action ϕ:[0,∞)×X→X\phi:[0,\infty)\times X\to X satisfying ϕ0=id⁡\phi_0=\operatorname{id} and ϕt+s=ϕt∘ϕs\phi_{t+s}=\phi_t\circ\phi_s for s,t≥0s,t\ge0.

仅用非负实数时间、满足恒同与时间复合律的连续演化；这里取半动力系统的连续时间情形。

Example

On [0,∞)[0,\infty), ϕt(x)=max⁡(x−t,0)\phi_t(x)=\max(x-t,0) is a semiflow with noninjective time maps.

Usage and distinctions

The cited Chinese source also allows discrete semigroup time; this record fixes continuous nonnegative time and does not assume reversibility.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gerald Teschl — Ordinary Differential Equations and Dynamical Systems§6.1 Dynamical systems, G=R+ semigroup convention · 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2.1.2，p.11：半动力系统 · Checked 2026-10-14
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