Algebro-geometric approach to an Okamoto transformation, the Painlevé VI and Schlesinger equations

DOI10.1007/s00023-019-00765-8zbMath1416.34077OpenAlexW2912117194MaRDI QIDQ1735500

Vasilisa Shramchenko, Vladimir Dragović

Publication date: 28 March 2019

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00023-019-00765-8

zbMATH Keywords

elliptic functionsisomonodromic deformationPainlevé equationsRiemann-Hilbert problems

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relationships between algebraic curves and integrable systems (14H70) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Elliptic functions and integrals (33E05) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items

Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics, Deformations of the Zolotarev polynomials and Painlevé VI equations, Note on algebro-geometric solutions to triangular Schlesinger systems

Cites Work

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• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• On Cayley's explicit solution to Poncelet's porism
• Self-dual \(SU(2)\)-invariant Einstein metrics and modular dependence of theta functions
• On orders of movable poles of the Schlesinger equation
• Monodromy of certain Painlevé-VI transcendents and reflection groups
• On the algebro-geometric integration of the Schlesinger equations
• On the tau-function for the Schlesinger equation of isomonodromic deformations.
• Twistor spaces, Einstein metrics and isomonodromic deformations
• Triangular Schlesinger systems and superelliptic curves
• Canonical structure and symmetries of the Schlesinger equations
• The meromorphic nature of the sixth Painlevé transcendents
• Poncelet Porisms and Beyond
• Kernel functions, analytic torsion, and moduli spaces
• Sixth Painlev\'e Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$
• Algebro-Geometric Solutions of the Schlesinger Systems and the Poncelet-Type Polygons in Higher Dimensions
• The elliptic representation of the general Painlevé VI equation
• Note on algebro-geometric solutions to triangular Schlesinger systems
• On Algebraic Solutions to Painleve VI
• A new hierarchy of integrable systems associated to Hurwitz spaces
• Picard and Chazy solutions to the Painlevé VI equation