单峰映射2~N周期解顺序的直接构造

有关种群生态学和其它某些学科中一类重要的差分方程,一维单峰映象的周期解,刘家冈给出了倍周期分岔2NP序列解的顺序表达式。本文将该公式化简并给出几个有趣的性质,最后给出一个不加任何计算直接写出2NP序列解的顺序的方法。讨论了中国古典“九连环”玩具装环顺序数和构形数之间也存在的同样对应。

A DIRECT FORMULATION OF ORDERING 2~N-PERIODIC SOLUTIONS OF A UNI-MODAL MAP

In this paper, the expression of 2N-periodic solutions order in a uni-modal one-dimensional map given by (l), was simplified. By using binary, expression, a direct structuring method of order, the solution was derived. It shows that the result exactly corresponds to the playing of a traditional toy the Chinese linked Rings,which can be expressed by binary numbering (2), with . N= number of rings, M=configuration number for rings=order of iteration of the map, and P=step number in ring -playing = order according to the magnitude of the map. An example for N= 4 is shown in fig.2.