Category:Definitions/Julia Sets

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This category contains definitions related to Julia Sets.
Related results can be found in Category:Julia Sets.


Let $f$ be an iterated rational function defined on the extended complex plane $\overline \C$.

Definition $1$

The Julia set of $f$ is the closed subset of $\overline \C$ which is invariant under $f$.


Definition $2$

The Julia set of $f$ is the boundary of the set of those points in $\overline \C$ whose orbits under $f$ are bounded.