Definition:Strange Attractor

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 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 $A$.

Examples

Hénon Attractor

The Hénon attractor is an example of a strange attractor.

Lorenz Attractor

The Lorenz attractor is an example of a strange attractor.

Also see

• Results about strange attractors can be found here.

Historical Note

The term strange attractor was introduced in $1971$ by David Pierre Ruelle and Floris Takens.

Sources

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