Inverse approach to study the planar polynomial vector field with algebraic solutions

DOI10.1088/0305-4470/37/12/009zbMath1049.34035OpenAlexW2093223904MaRDI QIDQ4466276

Natalia Sadovskaia, Rafael O. Ramírez

Publication date: 9 June 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/37/12/009

zbMATH Keywords

first integralpolynomial differential systemalgebraic limit cycles

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10)

Related Items (2)

The 16th Hilbert problem restricted to circular algebraic limit cycles ⋮ Normal forms of polynomial differential systems in \(\mathbb{R}^3\) having at least three invariant algebraic surfaces

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