Feigenbaum重正化群方程的准确解

ACCURATE SOLUTION OF THE FEIGENBAUM’S RENORMALIZATION GROUP EQUATION

重正化群方法是探讨Ｆｅｉｇｅｎｂａｕｍ普适常数机理的有效途径．本文给出了Ｆｅｉｇｅｎｂａｕｍ重正化群方程的一个准确解，它为分段分式线性函数．这是该类方程的连续可微解具有的最简单形式的解析表达式．本文同时给出了由计算机绘制的这个解的图象．该解的Ｓｃｈｗａｒｔｚ导数为零。

The renormalization group method is recognized as an effective way to explore the mathematics foundation of the Feigenbaum’s constant. In this paper, an accurate solution, g(x) , of the Feigenbaum’s renormalization group equation g(x)=-1λg(g(-λx)), g(0)=1, |g(x)|≤1, is found, it is a piecewise fractional linear function. This is the most simple expression of continuous and differentiable solution on such a class of functional equations.