minimal dynamical system

极小系统

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

Other names / variants: minimality · 极小性

Translation evidence: Literature usage

Meaning in context

A continuous self-map of a nonempty compact space is minimal when every forward orbit is dense in the whole space.

非空紧空间上的连续自映射，其每个点的正向轨道都在整个空间中稠密。

Example

Every irrational circle rotation is minimal.

Usage and distinctions

Transitivity needs open-set connections or, under suitable hypotheses, one dense orbit; minimality requires all forward orbits to be dense.

Recommended reading in this subject · Preparation & skip guidance

Definition 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）§2.3 轨道稠密性，定义2.3.1，p.17，连续映射情形 · 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）§2.3，p.17，定义2.3.1及“极小性”用语 · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.