This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.

A strange attractor is the limit set of a chaotic trajectory. A

strange attractor is an attractor that is topologically distinct from

a periodic orbit or a limit cycle. A strange attractor can be

considered a fractal attractor. An example of a strange attractor is

the Henon attractor.

Consider a volume in phase space defined by all the initial conditions

a system may have. For a dissipative system, this volume will shrink

as the system evolves in time (Liouville's Theorem). If the system is

sensitive to initial conditions, the trajectories of the points

defining initial conditions will move apart in some directions, closer

in others, but there will be a net shrinkage in volume. Ultimately,

all points will lie along a fine line of zero volume. This is the

strange attractor. All initial points in phase space which ultimately

land on the attractor form a Basin of Attraction. A strange attractor

results if a system is sensitive to initial conditions and is not

conservative.

Note: While all chaotic attractors are strange, not all strange

attractors are chaotic.

Reference:

1. Grebogi, et al., Strange Attractors that are not Chaotic, "Physica

D" 13 (1984), pp. 261-268.

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