Dynamical systems and ergodic theory Topological dynamics Concept
Minimal set
Summary
A minimal set of a continuous map is a nonempty closed invariant set that contains no smaller nonempty closed invariant set. Equivalently, the forward orbit of each of its points is dense in it. Minimal sets are the smallest building blocks of topological dynamics. On a nonempty compact space every continuous map has at least one minimal set, by Zorn's lemma.
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| Tag | CRGZZKQ7Z9 |
|---|---|
| URI | m2://CRGZZKQ7Z9 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37B05 |
| Specializes | Invariant set |
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