论文标题
在$ \ mathbb {c}^n $渐近曲线至正式曲线中的生物形态的稳定流形
Stable manifolds of biholomorphisms in $\mathbb{C}^n$ asymptotic to formal curves
论文作者
论文摘要
给定带有正式不变的曲线$γ$的Biholomormormormormormormormormormormormorm $ f \ in \ Mathrm {diff}（\ Mathbb {c}^n，0）$，使得乘数的乘数乘以受限的正式差异$ f |_γ$的乘数是Unity或unity或满足$ $ | f |_γ的根源，包含在$ f $的一套定期点中，或者存在一个有限的稳定流形$ f $的家族，其中所有轨道均为$γ$渐近，并且其联盟最终将每个轨道渐近造成$γ$。该结果概括为$γ$是正式的周期性曲线的情况。
Given a germ of biholomorphism $F\in\mathrm{Diff}(\mathbb{C}^n,0)$ with a formal invariant curve $Γ$ such that the multiplier of the restricted formal diffeomorphism $F|_Γ$ is a root of unity or satisfies $|(F|_Γ)'(0)|<1$, we prove that either $Γ$ is contained in the set of periodic points of $F$ or there exists a finite family of stable manifolds of $F$ where all the orbits are asymptotic to $Γ$ and whose union eventually contains every orbit asymptotic to $Γ$. This result generalizes to the case where $Γ$ is a formal periodic curve.
