alpha-limit set

α极限点集

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Other names / variants: alpha limit set

Translation evidence: Literature usage

Meaning in context

For a homeomorphism TT, α(x)\alpha(x) is the set of limits of T−nkxT^{-n_k}x along sequences nk→∞n_k\to\infty.

同胚下沿负向轨道、绝对时间趋于无穷的子序列所得的全部极限点。

Example

For the homeomorphism T(x)=x2T(x)=x^2 on [0,1][0,1] and 0<x<10<x<1, α(x)={1}\alpha(x)=\{1\} whereas ω(x)={0}\omega(x)=\{0\}.

Usage and distinctions

A noninvertible map does not specify one backward orbit; any extension requires a chosen past history.

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）§2.2，定义2.2.2及注2.2.1，p.13，负迭代子序列公式 · 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）§2.2，定义2.2.2，p.13：α极限点集 · Checked 2026-10-14
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