AN ALGORITHM FOR FINDING INVARIANT ALGEBRAIC CURVES OF A GIVEN DEGREE FOR POLYNOMIAL PLANAR VECTOR FIELDS

DOI10.1142/S0218127405012442zbMath1088.34023OpenAlexW2147988029MaRDI QIDQ5318383

Grzegorz Świrszcz

Publication date: 26 September 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127405012442

zbMATH Keywords

symbolic computationinvariant algebraic curvepolynomial system of two ordinary differential equations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (3)

Relationships between limit cycles and algebraic invariant curves for quadratic systems ⋮ Polynomial inverse integrating factors for quadratic differential systems ⋮ Classification of quadratic systems admitting the existence of an algebraic limit cycle

Cites Work

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• A family of non-Darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree
• A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals
• A computer-assisted proof of the Feigenbaum conjectures
• Uniqueness of algebraic limit cycles for quadratic systems

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