Asymptotic behavior of the fourth Painlevé transcendents in the space of initial values

DOI10.1007/s00365-016-9329-3zbMath1356.34093arXiv1412.3541OpenAlexW3160101666MaRDI QIDQ329462

Milena Radnović, Nalini Joshi

Publication date: 21 October 2016

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.3541

zbMATH Keywords

asymptotic behaviorresolution of singularitiesfourth Painlevé equationrational surfacespace of initial values

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30)

Related Items (7)

Global Asymptotics of the Sixth Painlevé Equation in Okamoto’s Space ⋮ Takasaki’s rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations ⋮ Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena ⋮ Poles of Painlevé IV rationals and their distribution ⋮ Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics ⋮ Space of initial conditions for a cubic Hamiltonian system ⋮ Asymptotic behaviour of the third Painlevé transcendents in the space of initial values

Cites Work

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• Okamoto's space for the first Painlevé equation in Boutroux coordinates
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• On some Hamiltonian structures of Painlevé systems. II
• Bäcklund transformations for fourth Painlevé hierarchies
• On the algebraic independence of generic Painlevé transcendents
• Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems
• Numerical studies of the fourth Painlevé equation
• Symmetries in the fourth Painlevé equation and Okamoto polynomials
• The fourth Painlevé equation and associated special polynomials
• Non-integrability of the fourth Painlevé equation in the Liouville–Arnold sense

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