论文标题
$（\ Mathbb {C}^2,0）$的可逆抛物线差异性
Reversible parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ and exceptional hyperbolic CR-singularities
论文作者
论文摘要
本文的目的是双重的：首先，我们研究了$（\ Mathbb {C}^2,0）$的抛物线差构型的全态细菌，这些抛物性差异是由全体形态反射逆转的，并具有与非核心关键点的分析第一积分。我们找到了一种规范的形式正常形式，并根据功能不变的收集提供了完整的分析分类（在正式的通用情况下）。它们限制了第一个积分的零基因座的不可回扣组成部分，从而减少了伯克霍夫 - Écalle-佛经元模量的一维限制性抛物线胚芽。 然后，我们将此分类也概括为$（\ Mathbb {C}^2,0）$的抗塑形差异性的细菌，其正方形迭代为上述形式。 与之相关的是，我们解决了$ \ mathbb {c}^2 $正式和分析分类的问题，其在表面上是全面的，即可以是固定的，即在$ holemorphermorphormorphormorphormorphermorphermorthyplplane n $ n $ n $ n $ n $ n $ cl中，具有非偏差的cr奇异性类型的奇异性cr奇异性奇异性。
The aim of this article is twofold: First we study holomorphic germs of parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ that are reversed by a holomorphic reflection and posses an analytic first integral with non-degenerate critical point at the origin. We find a canonical formal normal form and provide a complete analytic classification (in formal generic cases) in terms of a collection of functional invariants. Their restriction to an irreductible component of the zero locus of the first integral reduces to the Birkhoff--Écalle--Voronin modulus of the 1-dimensional restricted parabolic germ. We then generalize this classification also to germs of anti-holomorphic diffeomorphisms of $(\mathbb{C}^2,0)$ whose square iterate is of the above form. Related to it, we solve the problem of both formal and analytic classification of germs of real analytic surfaces in $\mathbb{C}^2$ with non-degenerate CR singularities of exceptional hyperbolic type, under the assumption that the surface is holomorphically flat, i.e. that it can be locally holomorphically embedded in a real hyperplane of $\mathbb{C}^2$.
