Duality between integrable Stäckel systems

DOI10.1088/0305-4470/32/45/311zbMath0989.37068arXivsolv-int/9812001OpenAlexW1978796081MaRDI QIDQ4947860

Andreĭ Vladimirovich Tsyganov

Publication date: 25 April 2000

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

Full work available at URL: https://arxiv.org/abs/solv-int/9812001

zbMATH Keywords

hyperelliptic curveKepler problemLax pairsAbel mapHenon-Heiles systems\(r\)-matrix algebrasintegrable determinationsintegrable Holt potentialintegrable Stäckel systems

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) 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)

Energy dependent integrability ⋮ Systematic construction of nonautonomous Hamiltonian equations of Painlevé‐type. II. Isomonodromic Lax representation ⋮ Integrable systems on a sphere, an ellipsoid and a hyperboloid ⋮ Transformation of the Stäckel matrices preserving superintegrability ⋮ The Maupertuis Principle and Canonical Transformations of the Extended Phase Space ⋮ On maximally superintegrable systems ⋮ Leonard Euler: addition theorems and superintegrable systems ⋮ One invariant measure and different Poisson brackets for two non-holonomic systems ⋮ On one integrable system with a cubic first integral ⋮ Stäckel equivalence of non-degenerate superintegrable systems, and invariant quadrics ⋮ Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta ⋮ Lax representations for separable systems from Benenti class ⋮ Equivalent integrable metrics on the sphere with quartic invariants

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