Movable algebraic singularities of second-order ordinary differential equations

DOI10.1063/1.3068414zbMath1202.34152arXiv0804.2859OpenAlexW3099083787MaRDI QIDQ3650455

Rodney G. Halburd, Galina Filipuk

Publication date: 14 December 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.2859

zbMATH Keywords

nonlinear differential equationsalgebraseries (mathematics)

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Related Items (12)

Regularising transformations for complex differential equations with movable algebraic singularities ⋮ Solution with movable singular points of some Hamiltonian system ⋮ Polynomial Hamiltonian systems with movable algebraic singularities ⋮ Takasaki’s rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations ⋮ On Hamiltonian structures of quasi-Painlevé equations ⋮ Poles of Painlevé IV rationals and their distribution ⋮ Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics ⋮ Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property ⋮ Rational ODEs with Movable Algebraic Singularities ⋮ On singularities of certain non-linear second-order ordinary differential equations ⋮ Movable singularities of equations of Liénard type ⋮ Regularising transformations for the \((n,n+1)\)-Liénard equations

Cites Work

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• A class of differential equations of PI-type with the quasi-Painlevé property
• Painlevé property of monodromy preserving deformation equations and the analyticity of \(\tau\) functions
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• Painlevé functions of the third kind
• A Direct Proof that Solutions of the Six Painlevé Equations Have No Movable Singularities Except Poles
• On the Singularities in the Complex Plane of the Solutions of yn+y′f(y)+g(y)=P(x)
• On Painlevé's equations I, II and IV
• Solutions of the first and second Painlevé equations are meromorphic

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