An algebraic geometric classification of superintegrable systems in the Euclidean plane

DOI10.1016/J.JPAA.2018.07.005zbMath1453.37058arXiv1602.07890OpenAlexW2963776440WikidataQ129368265 ScholiaQ129368265MaRDI QIDQ1634859

Konrad Schöbel, Jonathan M. Kress

Publication date: 18 December 2018

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.07890

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) Relationships between algebraic curves and integrable systems (14H70) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (7)

Projectively equivalent 2-dimensional superintegrable systems with projective symmetries ⋮ An algebraic geometric foundation for a classification of second-order superintegrable systems in arbitrary dimension ⋮ Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups ⋮ Algebraic conditions for conformal superintegrability in arbitrary dimension ⋮ Stäckel equivalence of non-degenerate superintegrable systems, and invariant quadrics ⋮ New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates ⋮ Dynamical symmetry algebras of two superintegrable two-dimensional systems

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