Non-integrability of some Painlevé VI-equations and dilogarithms

DOI10.1134/S1560354707060056zbMath1229.37057MaRDI QIDQ655295

Tsvetana Stoyanova, Emil Horozov

Publication date: 3 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

integrabilityHamiltonian systemPainlevé VI-equations

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (7)

Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena ⋮ Picard-Vessiot theory and integrability ⋮ Zero level perturbation of a certain third-order linear solvable ODE with an irregular singularity at the origin of Poincaré rank 1 ⋮ Galoisian methods for testing irreducibility of order two nonlinear differential equations ⋮ Painlevé equations, elliptic integrals and elementary functions ⋮ Variations for some Painlevé equations ⋮ The holonomy group at infinity of the Painlevé VI equation

Cites Work

• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• Rational solutions of the Painlevé VI equation
• Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
• On the Monodromy of Higher Logarithms
• Classical Polylogarithms

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