Definition:Julia Set/Definition 2
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Definition
Let $f$ be an iterated rational function defined on the extended complex plane $\overline \C$.
The Julia set of $f$ is the boundary of the set of those points in $\overline \C$ whose orbits under $f$ are bounded.
That is, it is the boundary of the filled Julia set of $f$.
Also see
- Results about Julia sets can be found here.
Source of Name
This entry was named for Gaston Maurice Julia.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Julia set
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Julia set