Category:Definitions/Attractors

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

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

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

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

An attractor is an invariant set $A$ in $X$ towards which nearby points $x$ converge, that is:

$T \sqbrk A = A$

$x_n = \map {T^n} x$ approaches $A$ as $n$ increases for points close to $A$.