C^2的形式可逆映射
Formally-Reversible Maps of C^2
摘要：
一个群的元素$g$称为{ \em可逆}，如果它在群中共轭到它的逆。本文研究复系数二元形式幂级数的形式可逆偶群$G$中的可逆性。主要结果是描述的通用可逆元素的$G$。我们列出两个显式序列的可逆性，它们之间的代表所有共轭类的可逆性。我们证明了每一个这样的元素是可逆的一些元素的有穷级，因此是产品的两个元素的有限偶数阶。那些可以被对合反转的元素称为{ \em强可逆}。我们也将这些。我们得出了一些结论一般可逆群的双全纯芽在两个变量，以及关于因式分解的形式地图的产品的可逆。具体地说，可逆性的每一个乘积都减少到5的乘积。
英文摘要：
An element $g$ of a group is called {\em reversible} if it is conjugate in the group to its inverse. This paper is about reversibles in the group $G$ of formally-invertible pairs of formal power series in two variables, with complex coefficients. The main result is a description of the generic reversible elements of $G$. We list two explicit sequences of reversibles which between them represent all the conjugacy classes of such reversibles. We show that each such element is reversible by some element of finite order, and hence is the product of two elements of finite even order. Those elements that may be reversed by an involution are called {\em strongly reversible}. We also characterise these. We draw some conclusions about generic reversibles in the group of biholomorphic germs in two variables, and about the factorization of formal maps as products of reversibles. Specifically, each product of reversibles reduces to the product of five.
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