Symmetries of the Garnier system and of the associated polynomial Hamiltonian system

DOI10.3792/pjaa.66.176zbMath0726.58025OpenAlexW2050034786MaRDI QIDQ804034

Hironobu Kimura

Publication date: 1990

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.66.176

zbMATH Keywords

Weyl groupcompletely integrable Hamiltonian systemgroup of symmetriesmonodromy preserving deformation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Pfaffian systems (58A17) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items

Toda equation and special polynomials associated with the Garnier system ⋮ A reduction of Hamiltonian systems with multi-time variables along a regular singularity ⋮ A Lax formulation of a generalized \(q\)-Garnier system ⋮ Unnamed Item ⋮ Bi-orthogonal systems on the unit circle, regular semi-classical weights and integrable systems. II ⋮ Discrete power functions on a hexagonal lattice I: derivation of defining equations from the symmetry of the Garnier system in two variables

Cites Work

• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• On the polynomial Hamiltonian structure of the Garnier systems
• ON PARTICULAR SOLUTIONS OF THE GARNIER SYSTEMS AND THE HYPERGEOMETRIC FUNCTIONS OF SEVERAL VARIABLES
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