On singularities of certain non-linear second-order ordinary differential equations

DOI10.1007/s00025-021-01577-1zbMath1490.34113OpenAlexW4200452255WikidataQ115389817 ScholiaQ115389817MaRDI QIDQ2072205

Thomas Kecker, Galina Filipuk

Publication date: 26 January 2022

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-021-01577-1

zbMATH Keywords

Painlevé testblowing up of singularitiesPainlevé-Ince equation

Mathematics Subject Classification ID

Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Related Items (4)

Regularising transformations for complex differential equations with movable algebraic singularities ⋮ A short note on the Painlevé XXV-Ermakov equation ⋮ Dynamics of the Painlevé-Ince equation ⋮ Regularising transformations for the \((n,n+1)\)-Liénard equations

Cites Work

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• Hidden symmetries and linearization of the modified Painlevé–Ince equation
• On the Singularities in the Complex Plane of the Solutions of yn+y′f(y)+g(y)=P(x)
• Solutions of the first and second Painlevé equations are meromorphic

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