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The logistic map is $f_\lambda(x)=\lambda x (1-x)$. It is known that the map is chaotic for $\lambda=4$ (on $[0;1]$) and also for $\lambda>0$ (on some hyperbolic subset of $[0,1]$). My question is:

For which parameters $\lambda \in (3,4)$ is the logistic map $f_\lambda$ chaotic?

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    $\begingroup$ I don't think there's a simple answer to that. There are infinitely many "windows" where it's not chaotic, infinitely many bands where it is, and a very intricate interplay between the two. en.wikipedia.org/wiki/Logistic_map will get you started. $\endgroup$
    – Gerry Myerson
    Commented Dec 9, 2019 at 11:21
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    $\begingroup$ The set of parameters for which it is chaotic is very complicated. The key word is "Mandelbrot set". $\endgroup$
    – Alexandre Eremenko
    Commented Dec 9, 2019 at 13:28

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