Bi-differential calculi, bi-Hamiltonian systems and conformal Killing tensors

DOI10.1088/0305-4470/33/48/313zbMath0967.37035OpenAlexW1965128684MaRDI QIDQ2703487

Mike Crampin, Willy Sarlet, Gerard Thompson

Publication date: 5 March 2001

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

Full work available at URL: https://doi.org/10.1088/0305-4470/33/48/313

zbMATH Keywords

bi-Hamiltonian systemsPoisson-Nijenhuis structuresbi-differential calculus

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson manifolds; Poisson groupoids and algebroids (53D17) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Infinite-dimensional manifolds (58B99)

Related Items (15)

A geometric approach to the separability of the Neumann-Rosochatius system ⋮ BIDIFFERENTIAL CALCULI, BICOMPLEX STRUCTURE AND ITS APPLICATION TO BIHAMILTONIAN SYSTEMS ⋮ Bi-Hamiltonian partially integrable systems ⋮ Quasi-Hamiltonian structure and Hojman construction ⋮ Lifting geometric objects to the dual of the first jet bundle of a bundle fibred over \(\mathbb R\) ⋮ Algebraic integrability conditions for Killing tensors on constant sectional curvature manifolds ⋮ Conformal Killing tensors with vanishing torsion and the separation of variables in the Hamilton--Jacobi equation ⋮ Unnamed Item ⋮ Lifted tensors and Hamilton-Jacobi separability ⋮ Killing tensors, warped products and the orthogonal separation of the Hamilton-Jacobi equation ⋮ Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems ⋮ A class of nonconservative Lagrangian systems on Riemannian manifolds ⋮ Bi-Hamiltonian systems of deformation type ⋮ Structural equations for a special class of conformal Killing tensors of arbitrary valence ⋮ Vanishing of the entropy pseudonorm for certain integrable systems

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