First integrals and normal forms for germs of analytic vector fields

DOI10.1016/j.jde.2008.06.002zbMath1166.34018OpenAlexW1968591061MaRDI QIDQ942178

Yingfei Yi, Xiang Zhang, Jian Chen

Publication date: 4 September 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.06.002

zbMATH Keywords

normal formresonancefirst integralanalytic vector field

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Explicit solutions, first integrals of ordinary differential equations (34A05) Dynamics induced by flows and semiflows (37C10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Related Items (15)

A note on local integrability of differential systems ⋮ Nonuniform dichotomy spectrum and normal forms for nonautonomous differential systems ⋮ A survey on local integrability and its regularity ⋮ Generalized rational first integrals of analytic differential systems ⋮ Analytic normalization of analytically integrable differential systems near a periodic orbit ⋮ Global C^∞ integrability of quartic–linear polynomial differential systems ⋮ Global \({C}^{\infty}\) integrability of cubic-linear polynomial differential systems ⋮ On polynomial integrability of the Euler equations on \(\mathfrak{so}(4)\) ⋮ Local integrability of Poincaré-Dulac normal forms ⋮ Analytic normalization of analytic integrable systems and the embedding flows ⋮ Formal first integrals for periodic systems ⋮ Varieties and analytic normalizations of partially integrable systems ⋮ Varieties of local integrability of analytic differential systems and their applications ⋮ Regularity and convergence of local first integrals of analytic differential systems ⋮ Nonexistence of formal first integrals for nonlinear systems under the case of resonance

Cites Work

• Convergence versus integrability in Poincaré-Dulac normal form
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• Convergence of Birkhoff normal forms for integrable systems
• Local first integrals of differential systems and diffeomorphisms
• Convergence or generic divergence of the Birkhoff normal form
• Period function for a class of Hamiltonian systems
• Nonexistence of isochronous centers in planar polynomial Hamiltonian systems of degree four
• Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance cases
• On non-integrability of general systems of differential equations
• Convergence versus integrability in Birkhoff normal form
• Extension of Floquet's theory to nonlinear periodic differential systems and embedding diffeomorphisms in differential flows
• Planar analytic systems having locally analytic first integrals at an isolated singular point
• Total convergence or general divergence in small divisors.
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