论文标题
全态功能的角图本地伪二轭物在其抛物线盆地
Horn maps of holomorphic functions locally pseudo-conjugate on their parabolic basins
论文作者
论文摘要
众所周知，具有简单的抛物线点的全态函数的喇叭图是一个完整的局部共轭不变。这是一个经典的结果，由Écalle，Voronin，Martinet和Ramis独立证明。 Lanford和Yampolski表明，如果两个功能$ f_1，f_2 $，简单的抛物线积分为$ z_1，z_2 $在其直接的抛物线盆地上进行全球结合，则结合及其相反的连续性及其逆连续为$ z_1 $。 $ z_2 $，那么他们的号角图必须是封面等效的：存在同构$ψ^+：\ Mathcal {d} _1^+\ to \ Mathcal {d} _2^+$和$ψ+$和$ψ^ - ：\ Mathcal {d}它们的域，以及圆柱上的翻译$ t $，使得$ \ mathbb {h} _2 \ circ Cycin^+ = t \ circ \ Mathbb {h} _1 $和$ \ Mathbb {在本文中，我们介绍了（半）局部共轭盆地的概念，我们将其称为本地伪偶联性，尤其没有做出任何连续性假设，并表明喇叭映射$ \ mathbb {h} h} _1 $ and $ \ mathbb {伪轭。该结果是通过抛物线重质化更好地理解不变类的第一步。
The lifted horn map of a holomorphic function with a simple parabolic point is well known to be a complete local conjugacy invariant; this is a classical result proved independently by Écalle, Voronin, Martinet and Ramis. Lanford and Yampolski have shown that, if two functions $f_1, f_2$ with simple parabolic points at $z_1, z_2$ are globally conjugate on their immediate parabolic basins, with the conjugacy and its inverse continuous at $z_1$, resp. $z_2$, then their horn maps must be cover-equivalent: there are isomorphisms $ψ^+ : \mathcal{D}_1^+\to \mathcal{D}_2^+$ and $ψ^- : \mathcal{D}_1^-\to \mathcal{D}_2^-$ between the top and bottom connected components of their domains, and a translation $T$ on the cylinder, such that $\mathbb{h}_2\circψ^+ = T\circ \mathbb{h}_1$ and $\mathbb{h}_2\circψ^- = T\circ \mathbb{h}_1$ holds on these domains. In this article, we introduce a notion of (semi) local conjugacy on immediate parabolic basins, which we call local pseudo-conjugacy and which in particular does not make any continuity assumption, and show that the horn maps $\mathbb{h}_1$ and $\mathbb{h}_2$ satisfy the condition above if and only if the two functions $f_1, f_2$ are locally pseudo-conjugate. This result is a first step to better understand invariant classes by parabolic renormalization.
