Dynamical systems and ergodic theory Complex dynamics Concept
Julia set
Summary
The Julia set of a rational function is the set of points near which the iterates of the function behave chaotically. It is the complement of the Fatou set, where the iterates form a normal family. For a map of degree at least it is a nonempty compact set. The map sends it onto itself, and it is often a fractal. Julia sets are the central objects of complex dynamics.
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| Tag | 5M4S7P04GR |
|---|---|
| URI | m2://5M4S7P04GR |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37F10 |
| Same as |
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Used by
- Quadratic polynomial dynamics
- External ray
- Lattès map
- Newton fractal
- Mandelbrot set
- Eremenko's conjecture