On the Poincaré problem

DOI10.1006/jdeq.2000.3801zbMath0974.34028OpenAlexW2017417276MaRDI QIDQ1582637

Sebastian Walcher

Publication date: 15 October 2000

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

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3801

zbMATH Keywords

polynomial vector fieldsalgebraic invariant curvesalgebraic integrating factors

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

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Cites Work

• Problèmes de modules pour des équations différentielles non linéaires du premier ordre
• Holomorphic foliations in \(CP(2)\) having an invariant algebraic curve
• Equations de Pfaff algébriques
• Invariant varieties through singularities of holomorphic vector fields
• On differential equations in normal form
• Algebraic invariant curves and the integrability of polynomial systems
• Elementary first integrals and algebraic invariant curves of differential equations
• Projections of polynomial vector fields and the Poincaré sphere
• The Poincaré problem in the nondicritical case
• Elementary First Integrals of Differential Equations
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Classification analytique des équations différentielles non linéaires résonnantes du premier ordre
• Holonomie et intégrales premières
• Invariant algebraic curves and conditions for a centre
• On algebraic solutions of algebraic Pfaff equations
• Symmetries and differential equations
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