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The birth of period three. (English) Zbl 0856.58012
In the logistic family \(x\to ax(1- x)\), what is the minimum value of \(a\) for which a cycle of period 3 exists? Of course, it is an algebraic number, but what exactly? The answer turns out to be \(1+ 2\sqrt 2\). An elementary and elegant proof is presented. The article also contains a popular introduction to the logistic family.

MSC:
37E99 Low-dimensional dynamical systems
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