Definition:Julia Set/Definition 2

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

• Equivalence of Definitions of Julia Set

• 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