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The key point here is that, any dynamical system that is not completely integrable will exhibit chaotic regimes1. In other words not all orbits will lie on an invariant torus (Liouville's torus is the topological structure of a fully integrable system), in principle a chaotic system can even have closed stable periodic orbits (typical for regular/integrable ...

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Self-similarity and chaos have been very influential in physics. They help us understand a lot of very interesting physical phenomena on the macroscopic scale, especially fluid flow and many-body problems. So, you can study these things and not be labelled a crank by physicists. But (you heard the "but" coming, right?) if you are talking about ...

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As the number of bifurcations goes to infinity, we can make some various claims. $$d_f={{\ln(N)} \over {\ln(s)}}$$ Where $d_f$ is the fractal dimension, N is the number of boxes, and s is the scale. (Examine $N\sim s^{d_f}$ to get the above) $$N=2^n$$ And $$s \sim {\delta_f}^n$$ Where $\delta_f$ is the Feigenbaum constant. We obtain, in the limit... ...

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There is no mention of chaos in the link you give. It is your description of what you read in the article using the everyday meaning of chaos. Chaos theory, copying from wikipedia is defined mathematically and belongs to the framework of classical physics. Small differences in initial conditions (such as those due to rounding errors in numerical ...

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