Repellor/Examples/Unit Circle under Complex Square Function

Example of Repellor

Consider the complex function $f: \C \to \C$ defined as:

$\forall z \in \C: \map f z = z^2$

Then the unit circle $\set {z \in \C: \size z = 1}$ of the Argand plane is a repellor.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): chaos
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): chaos