Difference between revisions of "Strange Attractors"

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[[Image:Lorenz-attractor-render-1-small.jpg|200px|right|thumb|The Lorenz Attractor]]An '''attractor''' is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.
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[[Image:Lorenz-attractor-render-1-small.jpg|200px|right|thumb|The Lorenz Attractor]]An '''attractor''' is a set to which a '''[[Dynamical Systems| dynamical system]]''' evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.
  
  

Revision as of 14:05, 30 May 2009

The Lorenz Attractor

An attractor is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.


An attractor is informally described as strange if it has non-integer dimension or if the dynamics on it are chaotic.

The Hénon Attractor

The term was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable.


Examples of strange attractors include the Hénon attractor, Rössler attractor, Lorenz Attractor, Tamari attractor.

Note: Must be edited... This is directly taken from wikipedia.