We treat three cubic recurrences, two of which generalize the famous iterated map $x \mapsto x (1-x)$ from discrete chaos theory. A feature of each asymptotic series developed here is a constant, dependent on the initial condition but otherwise intrinsic to the function at hand.

翻译：本文研究了三种三次递归关系，其中两种推广了离散混沌理论中著名的迭代映射$x \mapsto x (1-x)$。本文推导的每个渐近级数均具有一个特征常数，该常数依赖于初始条件，但除此之外完全由所研究函数本身的内在性质决定。