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I'm trying to delineate a minimal (and informal) "taxonomy" for classical continuous dynamical systems that could be interested by the phenomenon of "chaos" - unfortunately the sources I've found on the web are rarely compatible...

What I've understood is that if we adopt a strong definition of chaos (i.e. implying nonintegrability, strong mixing, dynamical instability - e.g. a K-system) then we have to suppose that there are too nonchaotic but ergodic/mixing systems, nonintegrable nonchaotic nonmixing ones, etc. If we limit our definition to dynamical instability (or - better - nonzero KS-entropy), we could get too nonmixing chaotic systems.

But there's Nekhoroshev's Theorem that says all nonintegrable systems will show at least a region of chaotic motion (Campbell, 1989), and in those regions motion is also strong mixing (Werndl, 2009).

How could those two different viewpoints be made compatible? And where am I wrong?

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