Stable Manifolds of Two-dimensional Biholomorphisms Asymptotic to Formal Curves

DOI10.1093/imrn/rnz143zbMath1487.32159arXiv1710.03728OpenAlexW3099924104WikidataQ127762142 ScholiaQ127762142MaRDI QIDQ5066809

Jasmin Raissy, Lorena López Hernanz, Javier Ribón, Fernando Sanz Sánchez

Publication date: 30 March 2022

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.03728

zbMATH Keywords

stable manifoldsgerms of holomorphic diffeomorphisms

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Local complex singularities (32S05)

Related Items (4)

Stable manifolds of biholomorphisms in Cn$\mathbb {C}^n$ asymptotic to formal curves ⋮ A fixed-point curve theorem for finite-orbits local diffeomorphisms ⋮ Characteristic directions of two-dimensional biholomorphisms ⋮ Birational properties of tangent to the identity germs without non‐degenerate singular directions

Cites Work

• Poincaré-Bendixson theorems for meromorphic connections and holomorphic homogeneous vector fields
• Parabolic curves for diffeomorphisms in \(\mathbb C^2\)
• Local structure of analytic transformations of two complex variables. I
• Attracting basins for automorphisms of \(\mathbb{C}^2\)
• Local structure of analytic transformations of two complex variables. II
• Parabolic curves of diffeomorphisms asymptotic to formal invariant curves
• The residual index and the dynamics of holomorphic maps tangent to the identity
• Parabolic curves in \(\mathbb{C}^3\)
• Index theorems for holomorphic self-maps
• Analytic transformations of \((\mathbb{C}^p,0)\) tangent to the identity
• New invariants and attracting domains for holomorphic maps in \(\mathbb{C}^2\) tangent to the identity
• Families of diffeomorphisms without periodic curves
• Degenerate characteristic directions for maps tangent to the identity
• On \'Ecalle-Hakim's theorems in holomorphic dynamics
• The dynamics of maps tangent to the identity and with nonvanishing index
• The dynamics near quasi-parabolic fixed points of holomorphic diffeomorphisms in C 2
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