“帐篷”映射的迭代问题研究

Iterations of tent maps

摘要:

帐篷映射作为非线性映射中较基础的一类, 其周期点问题使该映射成为人们的熟知，而其顶点作为破坏单调性的点在迭代下也有其变化规律. 本文讨论了帐篷映射在不同参数取值下顶点个数随迭代的变化. 在此基础上，本文给出了在参数a=0.5,b=(1+√5)/4特定情况下顶点个数的公式；并进一步给出了当b=1时，帐篷映射的n-周期点个数公式.

Abstract:

As a basic class of non-linear maps, tent maps is famous for their periodic point problem. And tent maps vertices as the points breaking the monotonicity in iterations have their own rules. This paper focuses on the change of the tent maps number of vertices under iterations, and gives the formula for the number of vertices in the specific case of parameter a=0.5,b=(1+√5)/4 and then the formula of the number of n-period points is given when b=1.