topological dynamical system

拓扑动力系统

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

Translation evidence: Literature usage

Meaning in context

In the discrete-time convention, a pair $(X,T)$ with a topological space $X$ and continuous self-map $T:X\to X$, whose evolution is given by the iterates of $T$.

按离散时间约定，由拓扑空间及其连续自映射组成、以该映射的迭代为演化的系统。

Example

The map $x\mapsto2x\bmod1$ defines a topological dynamical system on the circle.

Usage and distinctions

Some authors require a homeomorphism and two-sided time; continuous noninvertible maps are included here.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Gerald Teschl — Ordinary Differential Equations and Dynamical Systems§6.1 Dynamical systems, semigroup action and iterated-map example · Checked 2026-10-14

Translation sources

1. 李健、谭枫 — 关于 Li-Yorke δ-混沌与按序列分布 δ-混沌的等价性Printed p.34，正文首段：拓扑动力系统 · Checked 2026-10-14

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