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3.3] What do fractals have to do with chaos?




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This article is from the Nonlinear Science FAQ, by James D. Meiss jdm@boulder.colorado.edu with numerous contributions by others.

3.3] What do fractals have to do with chaos?

Often chaotic dynamical systems exhibit fractal structures in phase space.
However, there is no direct relation. There are chaotic systems that have
nonfractal limit sets (e.g. Arnold's cat map) and fractal structures that can
arise in nonchaotic dynamics (see e.g. Grebogi, C., et al. (1984). "Strange
Attractors that are not Chaotic." Physica 13D: 261-268.)

 

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