Deformations of the Zolotarev polynomials and Painlevé VI equations
DOI10.1007/s11005-021-01415-zzbMath1485.34212OpenAlexW3164274110MaRDI QIDQ2046821
Vasilisa Shramchenko, Vladimir Dragović
Publication date: 19 August 2021
Published in: Letters in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11005-021-01415-z
elliptic curvesGreen functionsannular domainsabelian differentialsZolotarev polynomialsharmonic measuresPainlevé VI equationsOkamoto transformations
Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relationships between algebraic curves and integrable systems (14H70) Elliptic functions and integrals (33E05) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)
Cites Work
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- Ellipsoidal billiards in pseudo-Euclidean spaces and relativistic quadrics
- Twists and generalized Zolotarev polynomials.
- Orthogonal- and Chebyshev polynomials on two intervals
- Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
- Pseudo-Riemannian geodesics and billiards
- Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
- Algebraic solution of a problem of E. I. Zolotarev and N. I. Akhiezer on polynomials with smallest deviation from zero
- Description of extremal polynomials on several intervals and their computation. II
- Monodromy of certain Painlevé-VI transcendents and reflection groups
- Green function, Painlevé VI equation, and Eisenstein series of weight one
- Algebro-geometric approach to an Okamoto transformation, the Painlevé VI and Schlesinger equations
- Caustics of Poncelet polygons and classical extremal polynomials
- Twistor spaces, Einstein metrics and isomonodromic deformations
- Periodic ellipsoidal billiard trajectories and extremal polynomials
- Periodic billiards within conics in the Minkowski plane and Akhiezer polynomials
- Extremal polynomials associated with a system of curves in the complex plane
- \`\` Real doubles\'\'\ of Hurwitz Frobenius manifolds
- Extremal Polynomials and Riemann Surfaces
- Minkowski plane, confocal conics, and billiards
- Chebyshev representation for rational functions
- Algebro-Geometric Solutions of the Schlesinger Systems and the Poncelet-Type Polygons in Higher Dimensions
- The elliptic representation of the general Painlevé VI equation
- Effective computation of Chebyshev polynomials for several intervals
- Combinatorial analysis of the period mapping: the topology of 2D fibres
