Definition:Repellor

Definition

Let $S$ be a dynamical system in a space $X$.

Let $T$ be an iterative mapping in $S$:

$x_{n + 1} = \map T {x_n}$

A repellor is an invariant set $A$ in $X$ towards which nearby points $x$ diverge.

Examples

Unit Circle under Complex Square Function

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.

Also see

• Definition:Attractor

• Results about repellors can be found here.

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