Global dynamics of the Kummer-Schwarz differential equation

DOI10.1007/s00009-013-0299-4zbMath1417.34040OpenAlexW2081682833WikidataQ115390418 ScholiaQ115390418MaRDI QIDQ2454112

Claudio Vidal, Jaume Llibre

Publication date: 12 June 2014

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-013-0299-4

zbMATH Keywords

integrabilityglobal dynamicsPoincaré compactificationKummer-Schwarz equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamics induced by flows and semiflows (37C10)

Related Items (4)

Dynamics of some three-dimensional Lotka-Volterra systems ⋮ Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie ⋮ On the generalizations of the Kummer-Schwarz equation ⋮ Saddle Invariant Objects and Their Global Manifolds in a Neighborhood of a Homoclinic Flip Bifurcation of Case B

Cites Work

• Symmetry and singularity properties of the generalised Kummer-Schwarz and related equa\-tions
• On the uniqueness of the Schwarzian and linearisation by nonlocal contact transformation
• The algebraic structure of the first integrals of third-order linear equations
• Qualitative theory of planar differential systems
• Bounded Polynomial Vector Fields
• Hidden and contact symmetries of ordinary differential equations

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