Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties

DOI10.1088/1751-8113/40/13/008zbMath1128.37037arXiv0708.3044OpenAlexW2113961227MaRDI QIDQ3431683

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

Publication date: 12 April 2007

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

Full work available at URL: https://arxiv.org/abs/0708.3044

Mathematics Subject Classification ID

Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relationships between surfaces, higher-dimensional varieties, and physics (14J81) 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) Surfaces and higher-dimensional varieties (14J99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (16)

Bôcher contractions of conformally superintegrable Laplace equations ⋮ An algebraic geometric classification of superintegrable systems in the Euclidean plane ⋮ On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals ⋮ Projectively equivalent 2-dimensional superintegrable systems with projective symmetries ⋮ 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 conditions for conformal superintegrability in arbitrary dimension ⋮ Toward a classification of semidegenerate 3D superintegrable systems ⋮ Leonard Euler: addition theorems and superintegrable systems ⋮ Toward classification of 2nd order superintegrable systems in 3-dimensional conformally flat spaces with functionally linearly dependent symmetry operators ⋮ Bôcher and abstract contractions of 2nd order quadratic algebras ⋮ Laplace-type equations as conformal superintegrable systems ⋮ Stäckel equivalence of non-degenerate superintegrable systems, and invariant quadrics ⋮ Behavior of a constrained particle on superintegrability of the two-dimensional complex Cayley-Klein space and its thermodynamic properties ⋮ On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields ⋮ N-dimensional Smorodinsky–Winternitz model and related higher rank quadratic algebra SW(N)

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