Algebraic Particular Integrals, Integrability and the Problem of the Center

DOI10.2307/2154430zbMath0777.58028OpenAlexW4241481000MaRDI QIDQ3137500

Dana Schlomiuk

Publication date: 8 December 1993

Full work available at URL: https://doi.org/10.2307/2154430

zbMATH Keywords

integrabilitycenterpolynomial systemquadratic systembifurcation diagramconstant of motionalgebraic particular integrals

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Local and nonlocal bifurcation theory for dynamical systems (37G99)

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Uses Software

• CoCoA

Cites Work

• Integrability of plane quadratic vector fields
• A method of constructing cycles without contact around a weak focus
• Ljapunov approach to multiple Hopf bifurcation
• Singularity theory and an introduction to catastrophe theory
• Classification and Analysis of two-dimensional real homogeneous quadratic differential equation systems
• Über das Auftreten von Wirbeln und Strudeln (geschlossener und spiraliger Integralkurven) in der Umgebung rationaler Unbestimmtheitsstellen
• A Counterexample to a Proposed Solution of Hilbert's Sixteenth Problem for Quadratic Systems
• Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems
• Liouvillian First Integrals of Differential Equations
• Generic Properties of Polynomial Vector Fields at Infinity
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