Julia Set for Square Function is Unit Circle

Theorem

The Julia set for the square function:

$\forall z \in \overline C: z \mapsto z^2$

is the unit circle.

Proof

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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