Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

DOI10.1016/j.na.2006.04.021zbMath1189.34065OpenAlexW2917649078MaRDI QIDQ880303

Laurent Cairó, Jaume Llibre

Publication date: 15 May 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.04.021

zbMATH Keywords

integrabilityphase portraitsrational first integralquadratic vector fields

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) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items

Nilpotent singular points and compactons, Limit cycles near hyperbolas in quadratic systems, Phase portraits of Abel quadratic differential systems of the second kind, 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, Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space \(\mathbb R^{12}\), The Second Hankel Determinant for k-symmetrical Functions, Evolutionary stable strategies and cubic vector fields, Stability and monotonicity of Lotka-Volterra type operators, Classification of global phase portrait of planar quintic quasi-homogeneous coprime polynomial systems, Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral, Global phase portraits and bifurcation diagrams for Hamiltonian systems of linear plus quartic homogeneous polynomials symmetric with respect to the \(y\)-axis, Quadratic system with a rational first integral of degree 2: a complete classification in the coefficient space \(\mathbb{R}^{12}\), Rational Integrability of the Maxwell–Bloch System, The classification on the global phase portraits of two-dimensional Lotka-Volterra system, Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems, Phase portraits of separable Hamiltonian systems, Phase portraits of Abel quadratic differential systems of second kind with symmetries, Polynomial inverse integrating factors for quadratic differential systems, Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3, Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems, THE GEOMETRY OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS AND AN INVARIANT STRAIGHT LINE, Bifurcations of travelling wave solutions for the Gilson-Pickering equation, PHASE PORTRAITS OF THE QUADRATIC SYSTEMS WITH A POLYNOMIAL INVERSE INTEGRATING FACTOR, The geometry of the real planar polynomial differential systems having their orbits embedded in conics, POLYNOMIAL VECTOR FIELDS IN ℝ³ WITH INFINITELY MANY LIMIT CYCLES

Cites Work

• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• On the integrability of two-dimensional flows
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• Phase portraits of planar semi-homogeneous vector fields-I
• Generic Properties of Polynomial Vector Fields at Infinity
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item