The Stäckel systems and algebraic curves

DOI10.1063/1.532789zbMath0989.37067arXivsolv-int/9712003OpenAlexW1971367360MaRDI QIDQ4701714

Andreĭ Vladimirovich Tsyganov

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9712003

zbMATH Keywords

matrix algebraintegrable systemshyperelliptic curvesLax pairsAbel-Jacobi mapWeierstrass reduction theoryStäckel matrix

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Jacobians, Prym varieties (14H40) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Algebraic geometry methods for problems in mechanics (70G55) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items (13)

Unnamed Item ⋮ One family of conformally Hamiltonian systems ⋮ Killing tensors with nonvanishing Haantjes torsion and integrable systems ⋮ The Maupertuis Principle and Canonical Transformations of the Extended Phase Space ⋮ On maximally superintegrable systems ⋮ Leonard Euler: addition theorems and superintegrable systems ⋮ Bäcklund transformations relating different Hamilton-Jacobi equations ⋮ One invariant measure and different Poisson brackets for two non-holonomic systems ⋮ Generalized Stäckel systems ⋮ The Kepler problem: polynomial algebra of nonpolynomial first integrals ⋮ Bi-Hamiltonian systems of natural form ⋮ Addition theorems and superintegrable systems ⋮ On the Chaplygin system on the sphere with velocity dependent potential

Cites Work

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• Quadrics on complex Riemannian spaces of constant curvature, separation of variables, and the Gaudin magnet
• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
• Integrability, Stäckel spaces, and rational potentials
• Lax representation for two-particle dynamics splitting on two tori
• Quasi-point separation of variables for the Henon - Heiles system and a system with a quartic potential
• Linear r-matrix algebra for classical separable systems
• Stationary problems for equation of the KdV type and dynamical r-matrices

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