Polynomial inverse integrating factors for quadratic differential systems

DOI10.1016/j.na.2010.04.004zbMath1203.34063OpenAlexW1990384308MaRDI QIDQ984060

Jaume Llibre, Bartomeu Coll, Antoni Ferragut

Publication date: 13 July 2010

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.2010.04.004

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) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) 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 (9)

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 ⋮ Classification of global phase portrait of planar quintic quasi-homogeneous coprime polynomial systems ⋮ Some new results on Darboux integrable differential systems ⋮ On the limit cycles bifurcating from an ellipse of a quadratic center ⋮ Bounding the number of remarkable values via Jouanolou's theorem ⋮ Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields ⋮ Planar semi-quasi homogeneous polynomial differential systems with a given degree ⋮ THE GEOMETRY OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS AND AN INVARIANT STRAIGHT LINE

Cites Work

• Unnamed Item
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• Polynomial first integrals of quadratic vector fields
• Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2
• Multiplicity of invariant algebraic curves in polynomial vector fields
• The full study of planar quadratic differential systems possessing a line of singularities at infinity
• Chordal quadratic systems
• On the integrability of two-dimensional flows
• Quadratic Hamiltonian vector fields
• Invariant algebraic curves linear in one variable for planar real quadratic systems.
• Darboux integrability and the inverse integrating factor.
• A family of non-Darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree
• On the shape of limit cycles that bifurcate from Hamiltonian centers
• Rational first integrals in the Darboux theory of integrability in \(\mathbb C^n\)
• Planar quadratic vector fields with invariant lines of total multiplicity at least five
• Polynomial inverse integrating factors for polynomial vector fields
• On the remarkable values of the rational first integrals of polynomial vector fields
• Darboux integrability and reversible quadratic vector fields
• Non-nested configuration of algebraic limit cycles in quadratic systems
• A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals
• PHASE PORTRAITS OF THE QUADRATIC SYSTEMS WITH A POLYNOMIAL INVERSE INTEGRATING FACTOR
• Liouvillian First Integrals of Differential Equations
• Integrable systems in the plane with center type linear part
• Invariant algebraic curves and conditions for a centre
• On the nonexistence, existence and uniqueness of limit cycles
• Darbouxian first integrals and invariants for real quadratic systems having an invariant conic
• AN ALGORITHM FOR FINDING INVARIANT ALGEBRAIC CURVES OF A GIVEN DEGREE FOR POLYNOMIAL PLANAR VECTOR FIELDS
• The shape of limit cycles that bifurcate from non-Hamiltonian centers
• About a conjecture on quadratic vector fields
• Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor

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