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arXiv 2002.071022020-02math.DSmath.CV

Stable manifolds of biholomorphisms in $\mathbb{C}^n$ asymptotic to formal curves

Lorena López-Hernanz, Javier Ribón, Fernando Sanz Sánchez, Liz Vivas

备注：: Part of section 5 in this article is an upgrade of some results in arXiv:1411.2945 that were not included in the final published version

英文摘要：

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.

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