topological entropy

拓扑熵

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

Translation evidence: Literature usage

Meaning in context

For continuous $T$ on a compact space, $h_{\mathrm{top}}(T)=\sup_{\mathcal U}\lim_{n\to\infty}n^{-1}\log N(\bigvee_{j=0}^{n-1}T^{-j}\mathcal U)$, where $\mathcal U$ ranges over finite open covers and $N$ is the least size of a subcover.

连续紧空间系统中，对有限开覆盖沿迭代拉回并联合加细，计算最小子覆盖数量的指数增长率，再对覆盖取上确界所得的量。

Example

The full binary shift has topological entropy $\log2$, using natural logarithms.

Usage and distinctions

The logarithm base determines units; topological entropy needs no selected invariant measure and differs from measure entropy.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Henk Bruin — Notes on Ergodic Theory§15.1 The original definition, equation (24) · Checked 2026-10-14

Translation sources

1. 何伟鲲 — 遍历论课程大纲（中国科学院大学）大纲内容，第三章 熵，第2节 拓扑熵 · Checked 2026-10-14

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

Open the reading guide for this concept