Quadratic systems with a polynomial first integral: A complete classification in the coefficient space \(\mathbb R^{12}\)

DOI10.1016/j.jde.2008.12.010zbMath1170.34003OpenAlexW2060163092MaRDI QIDQ1018374

Joan C. Artés, Jaume Llibre, Nicolae Vulpe

Publication date: 19 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.jde.2008.12.010

zbMATH Keywords

integrabilityrational first integralpolynomial first integralquadratic vector fieldsaffine invariant polynomial

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (10)

Quadratic differential systems with complex conjugate invariant lines meeting at a finite point ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Unnamed Item ⋮ Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space \(\mathbb R^{12}\) ⋮ On the polynomial differential systems having polynomial first integrals ⋮ Qualitative dynamics of five quadratic polynomial differential systems exhibiting five classical cubic algebraic curves ⋮ Phase portraits of planar piecewise linear refracting systems: focus-saddle case ⋮ Legendrian curves in \(\mathbb{C} P^3\): cubics and curves on a quadric surface ⋮ Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems ⋮ THE GEOMETRY OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS AND AN INVARIANT STRAIGHT LINE

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