Devaney chaos
Devaney混沌
Meaning in context
For a continuous self-map of an infinite compact metric space without isolated points, topological transitivity together with density of periodic points; these hypotheses imply sensitive dependence.
在无孤立点的无限紧致度量空间上，连续系统具有拓扑传递性且周期点稠密；在这些假设下敏感性可由二者推出。
Example
The full binary shift is Devaney chaotic by word concatenation and periodic repetition of words.
Usage and distinctions
Some definitions list sensitivity separately; always state the state-space assumptions, and do not equate this criterion with Li–Yorke chaos.
Read the encyclopedia explanation
Recommended reading in this subject · Preparation & skip guidance
Definition sources
- Gerald Teschl — Ordinary Differential Equations and Dynamical Systems§11.3, Devaney definition and Lemma 11.3 · Checked 2026-10-14
Translation sources
- 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.36，注记3(4)：Devaney混沌 · Checked 2026-10-14