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We review the fundamentals of coupling constant metamorphosis (CCM) and the St\"ackel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds.
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Kalnins E.G., Kress J.M., Miller W.Jr. and Pogosyan G.S., Completeness of superintegrability in two-dimensional constant curvature spaces. J. Phys. A: Math Gen
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Daskaloyannis C., Quadratic Poisson algebras of two-dimensional classical superintegrable systems and quadratic associate algebras of quantum superintegrable systems. J. Math. Phys
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Gravel S. and Winternitz P., Superintegrability with third-order integrals in quantum and classical mechanics. J. Math. Phys
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E.G. Kalnins, G.C. Williams, W. Miller, Jr. and G.S. Pogosyan, On superintegrable symmetry breaking potentials in n-dimensional Euclidean space, J. Phys. A: Math Gen
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E. G. Kalnins , J. M. Kress, W, Miller and P. Winternitz. Superintegrable systems in Darboux spaces. J. Math. Phys
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A.Ballesteros, F.Herranz, M.Santander and T.Sanz-Gil. Maximal superintegrability on N N -dimensional curved spaces. J.Phys
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S. Gravel. Hamiltonians separable in Cartesian coordinates and third-order integrals of motion. J. Math Phys
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Superintegrability in Classical and Quantum Systems, P. Tempesta, P. Winternitz, W. Miller, G. Pogosyan editors, AMS, 37, 2005
2005
Cited alongside, same era.
Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. I: 2D classical structure theory. J. Math. Phys
2005
Cited alongside, same era.
Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. II: The classical 2D Stäckel transform. J. Math. Phys
2005
Cited alongside, same era.
Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. III: 3D classical structure theory. J. Math. Phys
2005
Kalnins E. G.., Miller W. Jr and Post S., Wilson polynomials and the generic superintegrable system on the 2-sphere, J. Phys. A: Math. Theor
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Ballesteras A. and Herranz, F. J., Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature. J. Phys. A: Math. Theor
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Kalnins E.G., Kress J.M, and Miller W.Jr., Fine structure for 3D second order superintegrable systems: 3-parameter potentials. J. Phys. A: Math. Theor
2007
Later among the works it cites.
E.G. Kalnins, J.M. Kress, and W. Miller, Jr., Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties, J. Math. Phys
2007
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P.E. Verrier and N.W. Evans. A new superintegrable Hamiltonian. J. Math. Phys
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Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. V: 2D and 3D quantum systems. J. Math. Phys
2006
Cited alongside, same era.
Daskaloyannis C. and Ypsilantis K. Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold. J. Math Phys
2006
Cited alongside, same era.
Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. IV: The classical 3D Stäckel transform and 3D classification theory. J. Math. Phys
2006
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Daskaloyannis C. and Tanoudis Y. Quantum superintegrable systems with quadratic integrals on a two dimensional manifold. J. Math Phys
2007
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C. Quesne. Quadratic algebra approach to an exactly solvable position-dependent mass Schrödinger equation in two dimensions. SIGMA
2007
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2008
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2008
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F. Tremblay, A. V. Turbiner and P. Winternitz. An infinite family of solvable and integrable quantum systems on a plane. J. Phys. A: Math. Theor
2009
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