Attractor
An attractor is a Set of states (points in the Phase Space), invariant under the dynamics, towards whichneighboring states in a given Basin of Attraction asymptotically approach in the course of dynamic evolution. Anattractor is defined as the smallest unit which cannot be itself decomposed into two or more attractors with distinct Basins of Attraction. This restriction is necessary since a DynamicalSystem may have multiple attractors, each with its own Basin of Attraction.
Conservative systems do not have attractors, since the motion is periodic. For dissipative DynamicalSystems, however, volumes shrink exponentially so attractors have 0 volume in 
-D phase space.
A stable Fixed Point surrounded by a dissipative region is an attractor known as a Sink. Regular attractors(corresponding to 0 Lyapunov Characteristic Exponents) act as LimitCycles, in which trajectories circle around a limiting trajectory which they asymptotically approach, butnever reach. Strange Attractors are bounded regions of Phase Space (corresponding toPositive Lyapunov Characteristic Exponents) having zero Measure inthe embedding Phase Space and a Fractal Dimension. Trajectories within a Strange Attractor appear toskip around randomly.
See also Barnsley's Fern, Basin of Attraction, Chaos Game, Fractal Dimension, Limit Cycle,Lyapunov Characteristic Exponent, Measure, Sink (Map), Strange Attractor- Regression
- Regression Coefficient
- Regula Falsi
- Regular Function
- Regular Graph
- Regular Isotopy
- Regular Isotopy Invariant
- Regularity Theorem
- Regularized Beta Function
- Regularized Gamma Function
- Regular Local Ring
- Regular Number
- Regular Parameterization
- Regular Patch
- Regular Point
- Regular Polygon
- Regular Polyhedron
- Regular Prime
- Regular Ring
- Regular Sequence
- Regular Singularity
- Regular Singular Point
- Regular Surface
- Regular Triangle Center
- Regulus