orbit of a dynamical system

轨道

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

Other names / variants: forward orbit · 正半轨道

Translation evidence: Literature usage

Meaning in context

For a self-map $T$, the forward orbit of $x$ is $\{T^nx:n\ge0\}$; when $T$ is invertible, its full orbit is $\{T^nx:n\in\mathbb Z\}$.

自映射反复作用于一点得到的点集；非负迭代组成正半轨道，可逆时所有整数迭代组成完整轨道。

Example

Under $T(x)=x/2$, the forward orbit of $1$ is $\{1,1/2,1/4,\ldots\}$.

Usage and distinctions

An orbit is the visited set, not its closure or its limiting set; forward and full orbits must be distinguished.

Read the encyclopedia explanation

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）§2.1，定义2.1.6，p.12：轨道、正半轨道、负半轨道 · Checked 2026-10-14

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