On the singularities of the planar cubic polynomial differential systems and the Euler Jacobi formula

DOI10.1007/S12346-020-00435-9zbMath1461.34052OpenAlexW3096833888MaRDI QIDQ2219809

Claudia Valls, Jaume Llibre

Publication date: 21 January 2021

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-020-00435-9

zbMATH Keywords

singular pointtopological indexpolynomial differential systemsEuler-Jacobi formulaBerlinskii Theorem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Applications of operator theory to differential and integral equations (47N20)

Related Items (2)

Configurations of the topological indices of the planar polynomial differential systems of degree \((2,m)\) ⋮ The improved Euler–Jacobi formula and the planar cubic polynomial vector fields in ℝ²

Cites Work

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• Configurations of fans and nests of limit cycles for polynomial vector fields in the plane
• Euler-Jacobian formula for double points and applications to quadratic and cubic systems
• Index of a polynomial field
• A survey of quadratic systems
• On General Properties of Quadratic Systems
• Some Applications of the Euler-Jacobi Formula to Differential Equations
• The Euler-Jacobi formula and the planar quadratic-quartic polynomial differential systems

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