On the holonomic deformation of linear differential equations

DOI10.3792/pjaa.73.152zbMath0904.34005OpenAlexW2062502837MaRDI QIDQ1387925

Hiroyuki Kawamuko

Publication date: 19 January 1999

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.73.152

zbMATH Keywords

Hamiltonian systemPainlevé equationsmonodromy preserving deformation theoryFuchs problemholonomic deformation

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Linear ordinary differential equations and systems (34A30)

Cites Work

• The degeneration of the two dimensional Garnier system and the polynomial Hamiltonian structure
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• On the \(\tau \)-function of the Painlevé equations
• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Painlevé property of monodromy preserving deformation equations and the analyticity of \(\tau\) functions
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• On the polynomial Hamiltonian structure of the Garnier systems
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