\(C^ k\)-conjugacy of holomorphic flows near a singularity

DOI10.1007/BF02699194zbMath0625.57011MaRDI QIDQ579674

Marc Chaperon

Publication date: 1986

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1986__64__143_0

zbMATH Keywords

hyperbolicweakly hyperbolic\(C^ k\)-conjugacygerm of a holomorphic vector fieldHolomorphic conjugacyPoincaré domainS-normal formSiegel domain

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Foliations in differential topology; geometric theory (57R30) Dynamical systems with hyperbolic behavior (37D99) Complex spaces with a group of automorphisms (32M99)

Related Items (12)

Basic facts and naive questions ⋮ Singularities in dynamics: a catastrophic viewpoint ⋮ Smooth Gevrey normal forms of vector fields near a fixed point ⋮ Structure of leaves and the complex Kupka-Smale property ⋮ A forgotten theorem on \(\mathbb{Z}^k\times\mathbb{R}^m\)-action germs and related questions ⋮ Riemann surface laminations with singularities ⋮ Birth of attracting compact invariant submanifolds diffeomorphic to moment-angle manifolds in generic families of dynamics ⋮ Topological aspects of completely integrable foliations ⋮ Unique ergodicity of harmonic currents on singular foliations of \({\mathbb{P}^2}\) ⋮ Ergodic theorems for laminations and foliations: recent results and perspectives ⋮ \(C^ k\)-conjugacy of holomorphic flows near a singularity ⋮ Linearization of resonant vector fields

Cites Work

• Unnamed Item
• \(C^ k\)-conjugacy of holomorphic flows near a singularity
• The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold
• Smooth linearization of germs of \(\mathbb{R}^2\)-actions and holomorphic vector fields
• The topology of holomorphic flows with singularity

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