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SIGMA, 2012, Volume 8, 070, 12 pages (Mi sigma747)  

This article is cited in 9 scientific papers (total in 9 papers)

Superintegrable extensions of superintegrable systems

Claudia M. Chanua, Luca Degiovannib, Giovanni Rastellic

a Dipartimento di Matematica, Università di Torino, Torino, via Carlo Alberto 10, Italy
b Formerly at Dipartimento di Matematica, Università di Torino, Torino, via Carlo Alberto 10, Italy
c Independent researcher, cna Ortolano 7, Ronsecco, Italy

Abstract: 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.

DOI: https://doi.org/10.3842/SIGMA.2012.070

Full text: PDF file (343 kB)
Full text: http://emis.mi.ras.ru/.../070
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Bibliographic databases:

ArXiv: 1210.3126
MSC: 70H06; 70H33; 53C21
Received: July 30, 2012; in final form September 27, 2012; Published online October 11, 2012
Language:

Citation: Claudia M. Chanu, Luca Degiovanni, Giovanni Rastelli, “Superintegrable extensions of superintegrable systems”, SIGMA, 8 (2012), 070, 12 pp.

Citation in format AMSBIB
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\by Claudia M. Chanu, Luca Degiovanni, Giovanni Rastelli
\paper Superintegrable extensions of superintegrable systems
\jour SIGMA
\yr 2012
\vol 8
\papernumber 070
\totalpages 12
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rastelli G., “Extensions of Natural Hamiltonians”, 2nd international conference on mathematical modeling in physical sciences 2013 (ic-msquare 2013), Journal of Physics Conference Series, 490, ed. Vagenas E. Vlachos D., IOP Publishing Ltd, 2014, 012088  crossref  isi  scopus
    2. Chanu C.M. Degiovanni L. Rastelli G., “The Tremblay-Turbiner-Winternitz System as Extended Hamiltonian”, J. Math. Phys., 55:12 (2014), 122701  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Chanu C.M. Degiovanni L. Rastelli G., “Extensions of Hamiltonian Systems Dependent on a Rational Parameter”, J. Math. Phys., 55:12 (2014), 122703  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Claudia Maria Chanu, Luca Degiovanni, Giovanni Rastelli, “Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post–Winternitz System”, SIGMA, 11 (2015), 094, 9 pp.  mathnet  crossref
    5. Chanu C.M. Degiovanni L. Rastelli G., “Warped Product of Hamiltonians and Extensions of Hamiltonian Systems”, Xxxth international colloquium on group theoretical methods in physics (icgtmp) (group30), Journal of Physics Conference Series, 597, IOP Publishing Ltd, 2015, 012024  crossref  isi  scopus
    6. C. M. Chanu, L. Degiovanni, G. Rastelli, “Modified Laplace–Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion”, J. Math. Phys., 58:3 (2017), 033509  crossref  mathscinet  zmath  isi  scopus
    7. A. M. Escobar-Ruiz, J. C. Lopez Vieyra, P. Winternitz, “Fourth order superintegrable systems separating in polar coordinates. I. Exotic potentials”, J. Phys. A-Math. Theor., 50:49 (2017), 495206  crossref  mathscinet  zmath  isi  scopus
    8. C. M. Chanu, G. Rastelli, “Extended Hamiltonians and shift, ladder functions and operators”, Ann. Phys., 386 (2017), 254–274  crossref  mathscinet  zmath  isi  scopus
    9. Escobar-Ruiz A.M. Lopez Vieyra J.C. Winternitz P. Yurdusen I., “Fourth-Order Superintegrable Systems Separating in Polar Coordinates. II. Standard Potentials”, J. Phys. A-Math. Theor., 51:45 (2018), 455202  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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