On the configurations of the singular points and their topological indices for the spatial quadratic polynomial differential systems

DOI10.1016/j.jde.2020.07.022zbMath1454.34055OpenAlexW3087388776MaRDI QIDQ2003936

Claudia Valls, Jaume Llibre

Publication date: 13 October 2020

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

Full work available at URL: https://doi.org/10.1016/j.jde.2020.07.022

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) Explicit solutions, first integrals of ordinary differential equations (34A05) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

Related Items (3)

Configurations of the topological indices of the planar polynomial differential systems of degree \((2,m)\) ⋮ Uniqueness of the limit cycles for complex differential equations with two monomials ⋮ The improved Euler–Jacobi formula and the planar cubic polynomial vector fields in ℝ²

Cites Work

• Euler-Jacobian formula for double points and applications to quadratic and cubic systems
• Unsolved problems in geometry
• A survey of quadratic systems
• The Number of Polyhedral (3-Connected Planar) Graphs
• Some Applications of the Euler-Jacobi Formula to Differential Equations
• Basic Algebraic Geometry 1
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