Dynamical systems and ergodic theory Complex dynamics Concept
Fatou set
Summary
The Fatou set of a rational function is the open set of points near which its iterates behave in a stable, predictable way. Precisely, it is where the iterates form a normal family. Its complement is the Julia set. The map permutes the connected components of the Fatou set. The possible types of periodic components are completely classified.
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| Tag | C0N0XGC6GK |
|---|---|
| URI | m2://C0N0XGC6GK |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37F10 |
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Used by
- Sullivan's no wandering domains theorem
- Newton fractal
- Siegel disc
- Classification of Fatou components
- Herman ring
- Julia set