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Superintegrable extensions of superintegrable systems
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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A procedure to extend a superintegrable system into a new superintegrable one is systematically tested for the known systems on $\mathbb E^2$ and $\mathbb S^2$ and for a family of systems defined on constant curvature manifolds. The procedure results effective in many cases including Tremblay–Turbiner–Winternitz and three-particle Calogero systems.
Keywords: superintegrable Hamiltonian systems; polynomial first integrals. 
@article{SIGMA_2012_8_a69,
     author = {Claudia M. Chanu and Luca Degiovanni and Giovanni Rastelli},
     title = {Superintegrable extensions of superintegrable systems},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a69/}
}
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Claudia M. Chanu; Luca Degiovanni; Giovanni Rastelli. Superintegrable extensions of superintegrable systems. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a69/

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