The logistic map, whose iterations lead to period doubling and chaos as the control parameter, is increased and has three cases of the control parameter where exact solutions are known. In this paper, we show that general solutions also exist for other values of the control parameter. These solutions employ a special function, not expressible in terms of known analytical functions. A method of calculating this function numerically is proposed, and some graphs of this function are given, and its properties are discussed.

中文翻译：

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关于后勤图的精确解的注释

逻辑地图的迭代导致周期倍增和混乱作为控制参数，它增加了，并且有三种情况的控制参数已知精确解。在本文中，我们表明对于控制参数的其他值也存在通用解。这些解决方案采用了一种特殊功能，无法用已知的分析功能来表达。提出了一种数值计算该函数的方法，给出了该函数的一些图形，并讨论了其性质。