PHASE PORTRAITS OF THE QUADRATIC SYSTEMS WITH A POLYNOMIAL INVERSE INTEGRATING FACTOR

DOI10.1142/S0218127409023299zbMath1167.34324OpenAlexW2090053111MaRDI QIDQ3391939

Antoni Ferragut, Jaume Llibre, Bartomeu Coll

Publication date: 13 August 2009

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

Full work available at URL: https://doi.org/10.1142/s0218127409023299

zbMATH Keywords

Darboux theory of integrabilityquadratic differential systemspolynomial inverse integrating factor

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Explicit solutions, first integrals of ordinary differential equations (34A05) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02) Equivalence and asymptotic equivalence of ordinary differential equations (34C41)

Related Items (7)

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ A new algorithm for finding rational first integrals of polynomial vector fields ⋮ A survey on the inverse integrating factor ⋮ Phase portraits of planar piecewise linear refracting systems: focus-saddle case ⋮ Global phase portraits and bifurcation diagrams for Hamiltonian systems of linear plus quartic homogeneous polynomials symmetric with respect to the \(y\)-axis ⋮ Polynomial inverse integrating factors for quadratic differential systems ⋮ THE GEOMETRY OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS AND AN INVARIANT STRAIGHT LINE

Cites Work

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• New sufficient conditions for a center and global phase portraits for polynomial systems
• Polynomial first integrals of quadratic vector fields
• Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2
• The full study of planar quadratic differential systems possessing a line of singularities at infinity
• Phase portaits of the quadratic vector fields with a polynominal first integral
• Chordal quadratic systems
• On the integrability of two-dimensional flows
• Planar quadratic vector fields with invariant lines of total multiplicity at least five
• Polynomial inverse integrating factors for polynomial vector fields
• Darboux integrability and reversible quadratic vector fields

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