On the vanishing set of inverse integrating factors

DOI10.1007/BF02969478zbMath1032.34027OpenAlexW1976793000MaRDI QIDQ5951663

Hector J. Giacomini, Lucio R. Berrone

Publication date: 4 March 2004

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02969478

zbMATH Keywords

critical pointplanar ordinary differential equationintegrating factorseparatrix cycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamics induced by flows and semiflows (37C10) Linear first-order PDEs (35F05) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (14)

Algebraic first integrals of the polynomial systems satisfying the Cauchy-Riemann conditions ⋮ A survey on the inverse integrating factor ⋮ The Poincaré map of degenerate monodromic singularities with Puiseux inverse integrating factor ⋮ Localizing attractors via a generalized La Salle principle ⋮ Some new results on Darboux integrable differential systems ⋮ On the remarkable values of the rational first integrals of polynomial vector fields ⋮ Integral characterization for Poincaré half-maps in planar linear systems ⋮ The inverse integrating factor and the Poincaré map ⋮ Generalized Hopf bifurcation for planar vector fields via the inverse integrating factor ⋮ Periodic solutions of second-order differential equations with two-dimensional Lie point symmetry algebra ⋮ Center problem with characteristic directions and inverse integrating factors ⋮ An integrating factor of the Darboux differential systems ⋮ Inverse Jacobi multipliers ⋮ Integral invariants and limit sets of planar vector fields

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• Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor

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