sensitive dependence on initial conditions

敏感依赖于初始条件

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Translation evidence: Literature usage

Meaning in context

For a map of a metric space, some $\delta>0$ has the property that for every $x$ and every neighborhood $U$ of $x$, there exist $y\in U$ and $n\ge0$ with $d(T^nx,T^ny)>\delta$.

存在统一的正分离尺度，使每个点的任意邻域内都能找到某个点，二者的某次迭代距离超过该尺度。

Example

On $(0,\infty)$ the map $T(x)=2x$ is sensitive, although it is not topologically transitive.

Usage and distinctions

Sensitivity alone is not Devaney chaos; on noncompact spaces it can depend on the chosen compatible metric.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Gerald Teschl — Ordinary Differential Equations and Dynamical Systems§11.3, sensitive-dependence definition and expanding noncompact example · Checked 2026-10-14

Translation sources

1. 黎日松 — 关于 f×f 与 f 的动力性质间关系的研究Printed p.23，定理5之后注记1）：敏感依赖于初始条件 · Checked 2026-10-14

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