Invariant Classification and Limits of Maximally Superintegrable Systems in 3D

Abstract

The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian manifolds can be obtained from singular limits of a generic system on the sphere. By using the invariant classification, the limits are geometrically motivated in terms of transformations of roots of the classifying polynomials.

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• Superintegrable Systems on 3 Dimensional Conformally Flat Spaces
• Bôcher Contractions of Conformally Superintegrable Laplace Equations
• An Algebraic Geometric Foundation for a Classification of Superintegrable Systems in Arbitrary Dimension
• $N$-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra $\mathcal{S}\mathcal{W}(N)$
• Algebraic Conditions for Conformal Superintegrability in Arbitrary Dimension
• Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras
• Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras
• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
• Projectively equivalent 2-dimensional superintegrable systems with projective symmetries
• Bocher contractions of conformally superintegrable Laplace equations: Detailed computations
• Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras
• Laplace equations, conformal superintegrability and Bôcher contractions
• Contractions of Degenerate Quadratic Algebras, Abstract and Geometric