Darboux integrability and the inverse integrating factor.
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Publication:1413199
DOI10.1016/S0022-0396(03)00190-6zbMath1043.34001MaRDI QIDQ1413199
Javier Chavarriga, Jaume Giné, Jaume Llibre, Hector J. Giacomini
Publication date: 16 November 2003
Published in: Journal of Differential Equations (Search for Journal in Brave)
Darboux integrabilityinverse integrating factorrational first integralpolynomial first integralecstatic curveremarkable values
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05) Dynamics induced by flows and semiflows (37C10)
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Cites Work
- Unnamed Item
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- Unnamed Item
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- Unnamed Item
- Equations de Pfaff algébriques
- On the integrability of two-dimensional flows
- Algebraic invariant curves and the integrability of polynomial systems
- Elementary first integrals and algebraic invariant curves of differential equations
- The limit cycle of the van der Pol equation is not algebraic
- Algebraic solutions for polynomial systems with emphasis in the quadratic case
- On the shape of limit cycles that bifurcate from Hamiltonian centers
- On the nonexistence of constants of derivations: the proof of a theorem of Jouanolou and its development
- On non-integrability of general systems of differential equations
- An improvement to Darboux integrability theorem for systems having a center
- Elementary First Integrals of Differential Equations
- Algebraic Particular Integrals, Integrability and the Problem of the Center
- Liouvillian First Integrals of Differential Equations
- On a new type of bifurcation of limit cycles for a planar cubic system
- 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
- On algebraic solutions of algebraic Pfaff equations
- The shape of limit cycles that bifurcate from non-Hamiltonian centers
- Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor
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