Compactification and desingularization of spaces of polynomial Liénard equations

DOI10.1016/j.jde.2005.08.011zbMath1105.34015OpenAlexW2018800950MaRDI QIDQ2493084

Freddy Dumortier

Publication date: 9 June 2006

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

Full work available at URL: https://doi.org/10.1016/j.jde.2005.08.011

zbMATH Keywords

compactificationsingular perturbationlimit cycledesingularizationLiénard equationHilbert's 16th problemHamiltonian perturbation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Perturbations of ordinary differential equations (34D10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Singular perturbations of ordinary differential equations (34D15)

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Cites Work

• Unnamed Item
• Polynomial Liénard equations near infinity
• Hilbert's 16th problem for quadratic vector fields
• Mathematical problems for the next century
• Putting a boundary to the space of Liénard equations
• Qualitative theory of planar differential systems

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