Limit relation between Toda chains and the elliptic \(\mathrm{SL}(N,\mathbb{C})\) top

DOI10.1007/s11232-012-0056-zzbMath1417.37196OpenAlexW1985902500MaRDI QIDQ2636617

G. A. Aminov

Publication date: 30 January 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-012-0056-z

zbMATH Keywords

Painlevé equationintegrable systemtopological structurenonautonomous system

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Integrable cases of motion in rigid body dynamics (70E40) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56) Higher-dimensional generalizations in rigid body dynamics (70E45)

Related Items

Degenerating the elliptic Schlesinger system ⋮ New \(2\times 2\)-matrix linear problems for the Painlevé equations III, V

Cites Work

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• Completely integrable Hamiltonian systems associated with matrix operators and abelian varieties
• Painlevé VI, rigid tops and reflection equation
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Integrable \(sl(N,\mathbb C)\) tops as Calogero-Moser systems
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• Lie algebras and Lax equations with spectral parameter on an elliptic curve
• The finite Toda lattices
• Three integrable Hamiltonian systems connected with isospectral deformations
• Algebraic curves and commuting matricial differential operators
• Integration of nonlinear equations by the methods of algebraic geometry
• Gaudin model, KZ equation and an isomonodromic problem on the torus
• Hitchin systems -- symplectic Hecke correspondence and two-dimensional version
• Integrable many-body systems via the Inosemtsev limit
• Elliptic linear problem for the Calogero--Inozemtsev model and Painlevé VI equation
• Painlevé–Calogero correspondence revisited
• Reduction of the elliptic SL(N,\mathbb C) top
• Elliptic Schlesinger system and Painlevé VI
• On the Toda Lattice. II: Inverse-Scattering Solution
• The Toda lattice. II. Existence of integrals

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