RT info:eu-repo/semantics/article
T1 Stable manifolds of biholomorphisms in Cn$\mathbb {C}^n$ asymptotic to formal curves
A1 López‐Hernanz, Lorena
A1 Ribón, Javier
A1 Sanz‐Sánchez, Fernando
A1 Vivas, Liz
AB Given a germ of biholomorphism 𝐹 ∈ Dif f (ℂ𝑛, 0) with aformal invariant curve Γ such that the multiplier of therestricted formal diffeomorphism 𝐹|Γ is a root of unityor satisfies |(𝐹|Γ)′(0)| < 1, we prove that either Γ is containedin the set of periodic points of 𝐹 or there exists afinite family of stable manifolds of 𝐹 where all the orbitsare asymptotic toΓ andwhose union eventually containsevery orbit asymptotic to Γ. This result generalizes to thecase where Γ is a formal periodic curve.
PB Wiley
SN 0024-6115
YR 2022
FD 2022
LK https://uvadoc.uva.es/handle/10324/68107
UL https://uvadoc.uva.es/handle/10324/68107
LA eng
NO Proc. London Math. Soc. (3) 2022;125:277–317.
DS UVaDOC
RD 23-nov-2024