论文标题
抛物线线生物形态细菌的球形正常形式
Spherical normal forms for germs of parabolic line biholomorphisms
论文作者
论文摘要
我们解决了固定点附近的复合线切线映射的全体形态细菌的反问题。我们提供了一个优先的（一组）抛物线图$δ$实现给定的Birkhoff-{é} Calle-Voronin模量$ψ$，并证明了它在我们介绍的功能类中的独特性。细菌是Gevrey正式矢量场的Time-1图，该图在覆盖Riemann Sphere的一对无限扇区上承认了Meromorormormormormormormormormormormormormormormorormorthics。因此，$δ$的分析延续是一张多估计的地图，该地图承认有限的单个分支机构有限的分支点。尤其是$δ$在包含0（初始固定点）和$ \ infty $的开放缝隙球上是全态和注射剂，其中属于伴侣抛物线$ \ frac {-1} {\ id} $。事实证明，在$ \ infty $上，抛物线胚芽的birkhoff-{é} calle-voronin模量是$ \ infty $是0的反向$ψ^{\ Circ-1} $。
We address the inverse problem for holomorphic germs of a tangent-to-identity mapping of the complex line near a fixed point. We provide a preferred (family of) parabolic map $Δ$ realizing a given Birkhoff--{É}calle-Voronin modulus $ψ$ and prove its uniqueness in the functional class we introduce. The germ is the time-1 map of a Gevrey formal vector field admitting meromorphic sums on a pair of infinite sectors covering the Riemann sphere. For that reason, the analytic continuation of $Δ$ is a multivalued map admitting finitely many branch points with finite monodromy. In particular $Δ$ is holomorphic and injective on an open slit sphere containing 0 (the initial fixed point) and $\infty$, where sits the companion parabolic point under the involution $\frac{-1}{\id}$. It turns out that the Birkhoff--{É}calle-Voronin modulus of the parabolic germ at $\infty$ is the inverse $ψ^{\circ-1}$ of that at 0.
