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SIGMA, 2012, Volume 8, 031, 9 pages (Mi sigma708)  

This article is cited in 5 scientific papers (total in 5 papers)

Superintegrable Stäckel systems on the plane: elliptic and parabolic coordinates

Andrey V. Tsiganov

St. Petersburg State University, St. Petersburg, Russia

Abstract: Recently we proposed a generic construction of the additional integrals of motion for the Stäckel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for elliptic and parabolic coordinate systems on the plane.

Keywords: integrability, superintegrability, separation of variables, Abel equations, addition theorems.

DOI: https://doi.org/10.3842/SIGMA.2012.031

Full text: PDF file (273 kB)
Full text: http://emis.mi.ras.ru/.../031
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Bibliographic databases:

ArXiv: 1204.1801
MSC: 37J35, 70H06
Received: April 10, 2012; in final form May 21, 2012; Published online May 25, 2012
Language:

Citation: Andrey V. Tsiganov, “Superintegrable Stäckel systems on the plane: elliptic and parabolic coordinates”, SIGMA, 8 (2012), 031, 9 pp.

Citation in format AMSBIB
\Bibitem{Tsi12}
\by Andrey V. Tsiganov
\paper Superintegrable St\"ackel systems on the plane: elliptic and parabolic coordinates
\jour SIGMA
\yr 2012
\vol 8
\papernumber 031
\totalpages 9
\mathnet{http://mi.mathnet.ru/sigma708}
\crossref{https://doi.org/10.3842/SIGMA.2012.031}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2942808}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000304404800001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84882345059}


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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. Grigoriev Yu.A., Tsiganov A.V., “On Superintegrable Systems Separable in Cartesian Coordinates”, Phys. Lett. A, 382:32 (2018), 2092–2096  crossref  mathscinet  isi  scopus
    2. A. V. Tsiganov, “Superintegrable systems with algebraic and rational integrals of motion”, Theoret. and Math. Phys., 199:2 (2019), 659–674  mathnet  crossref
    3. Tsiganov A.V., “Elliptic Curve Arithmetic and Superintegrable Systems”, Phys. Scr., 94:8 (2019), 085207  crossref  isi
    4. Tsiganov A.V., “Transformation of the Stackel Marices Preserving Superintegrability”, J. Math. Phys., 60:4 (2019), 042701  crossref  mathscinet  zmath  isi  scopus
    5. Bienayme O., “Integrals of Motion For Non-Axisymmetric Potentials”, Astron. Astrophys., 627 (2019), A123  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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