Category:Definitions/Strange Attractors

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

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

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

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

A strange attractor under $T$ is an infinite invariant set $A$ in $X$, usually an attractor, with additional properties:

$(1): \quad$ The orbits of $T$ exhibit sensitive dependence on initial conditions

$(2): \quad$ There exists an open set of points which are attracted to $A$.