Structure theory for second order 2D superintegrable systems with 1-parameter potentials

DOI10.3842/SIGMA.2009.008zbMath1195.81070arXiv0901.3081MaRDI QIDQ1016724

Ernest G. Kalnins, Willard jun. Miller, Sarah Post, Jonathan M. Kress

Publication date: 21 May 2009

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.3081

zbMATH Keywords

quadratic algebrassuperintegrability

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) Groups and algebras in quantum theory and relations with integrable systems (81R12) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Poisson algebras (17B63)

Related Items (8)

Generalized quadratic commutator algebras of PBW-type ⋮ An algebraic geometric classification of superintegrable systems in the Euclidean plane ⋮ Doubly exotic \(N\)th-order superintegrable classical systems separating in Cartesian coordinates ⋮ An algebraic geometric foundation for a classification of second-order superintegrable systems in arbitrary dimension ⋮ Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces ⋮ Algebraic conditions for conformal superintegrability in arbitrary dimension ⋮ Laplace-type equations as conformal superintegrable systems ⋮ Superintegrable systems with spin and second-order tensor and pseudo-tensor integrals of motion

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