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In Wikipedia’s article ‘List of chaotic maps’ (https://en.wikipedia.org/wiki/List_of_chaotic_maps), one of the entries is:

Feigenbaum strange nonchaotic map

So, how is this possible?

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    $\begingroup$ map can be chaotic for some values of parameter and non-chaotic for other values. $\endgroup$ – Adam Dec 11 '18 at 18:02
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It depends strongly in what do you mean about chaos. The term chaos is not too well defined yet. "no universally accepted mathematical definition of chaos exists", this in an extract of this page:

https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics

There are also some definitions of chaos that you can try to verify to the function that you said.

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