About the Poincaré-Lyapunov theorem and necessary conditions for the existence of a center

DOI10.1016/j.crma.2009.07.009zbMath1194.34046OpenAlexW2105225097MaRDI QIDQ1032836

Driss Boularas

Publication date: 5 November 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.07.009

zbMATH Keywords

center-focus problemPoincaré-Lyapunov theoremplanar analytic vector fields

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Cites Work

• The nondegenerate center problem and the inverse integrating factor
• Équations d'amorçage d'intégrales premières formelles
• Successive derivatives of a first return map, application to the study of quadratic vector fields
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