Although the double pendulum is the poster boy of Chaos Theory, there are actually two "special" modes of oscillation (called "eigenmodes") in which the masses move in perfect harmonypic.twitter.com/CnivjtF8Hg
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So what I'm getting is, with a chaotic system like the double pendulum, any small perturbation from any initial point will eventually diverge exponentially from the original trajectory, right? So these aren't stable modes of oscillation
well no they can't be stable since it's a chaotic system .. if you perturb it you're essentially getting a new pendulum with new initial conditions
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I'm not sure you have to have sdic everywhere. Some systems with single point attractors have neighborhoods around them which don't have sdic. And only the boundary is really the chaotic part.
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For example, the three-body problem mostly has chaotic solutions but the figure eight is stable IIRC
End of conversation
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