This survey provides an overview of the existence of stable manifolds for tangent to the identity biholomorphisms in $(\mathbb{C}^2,0$) and its connection with the existence of invariant curves for formal vector fields.
Ce survey présente un aperçu de l’existence de variétés stables pour les biholomorphismes tangents à l’identité dans $(\mathbb{C}^2,0)$ et de son lien avec l’existence de courbes invariantes pour les champs de vecteurs formels.
Lorena López-Hernanz 1
CC-BY-ND 4.0
Lorena López-Hernanz. Local dynamics of tangent to the identity biholomorphisms in dimension two. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2026), pp. 129-147. doi: 10.5802/pmb.74
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author = {Lorena L\'opez-Hernanz},
title = {Local dynamics of tangent to the identity biholomorphisms in dimension two},
journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
pages = {129--147},
year = {2026},
publisher = {Presses universitaires de Franche-Comt\'e},
doi = {10.5802/pmb.74},
language = {en},
url = {https://pmb.centre-mersenne.org/articles/10.5802/pmb.74/}
}
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