关于N型映射的迭代和终于不动点

Iteration and final fixed point of N type mapping

函数迭代通常会发生复杂的动力学现象,即使是简单的函数,甚至是逐段的线性函数的迭代都很复杂.通常计算出一个分段线性函数的n次迭代精确表达式非常困难.本文考虑N型映射的动力学性质,定义了一个关于N型映射的指标函数.利用这个指标函数,本文给出了该映射n次迭代精确表达式,同时给出了终于不动点恰好第n步映到不动点的充分必要条件.

Complex dynamic phenomena usually occur in function iteration. Even simple functions and even the iteration of piecewise linear functions are very complex. It is usually very difficult to calculate the exact expression of n iterations of a piecewise linear function. In this paper, we consider the dynamic properties of N type mappings and define an index function for N type mappings. Using this index function, we give the exact expression of the n iterations of the mapping, and give the necessary and sufficient condition that the point is finally mapped to the fixed point at the n step.