From an iteration formula to Poincaré’s Isochronous Center Theorem for holomorphic vector fields

DOI10.1090/S0002-9939-07-08802-8zbMath1129.37027arXivmath/0511622OpenAlexW2024475644MaRDI QIDQ5291934

Guang Yuan Zhang

Publication date: 19 June 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511622

zbMATH Keywords

ordinary differential equationsholomorphic dynamics

Mathematics Subject Classification ID

Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (3)

The Briot-Bouquet systems and the center families for holomorphic dynamical systems ⋮ Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems

Cites Work

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• On periodic solutions of polynomial O.D.E.'s in the plane
• Conformal equivalence of analytic flows
• The centre conditions for a certain cubic system
• Dynamics of commuting systems on two-dimensional manifolds
• Isochronous Centers in Planar Polynomial Systems
• regularity properties of the period function near a center of a planar vector field
• Centre families in two–dimensional complex holomorphic dynamical systems
• Isochronous Systems and Perturbation Theory

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