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Regular and Chaotic Dynamics, 2009, Volume 14, Issue 3, Pages 389–406
DOI: https://doi.org/10.1134/S1560354709030034
(Mi rcd588)
 

This article is cited in 19 scientific papers (total in 19 papers)

Leonard Euler: Addition Theorems and Superintegrable Systems

A. V. Tsiganov

St. Petersburg State University, Petrodvorets, Ulyanovskaya str. 1, St. Petersburg 198504, Russia
Citations (19)
Abstract: We consider the Euler approach to constructing to investigating of the superintegrable systems related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stäckel systems.
Keywords: superintegrable systems, addition theorems.
Received: 24.10.2008
Accepted: 06.12.2008
Bibliographic databases:
Document Type: Article
MSC: 70H06, 70H20, 35Q72
Language: English
Citation: A. V. Tsiganov, “Leonard Euler: Addition Theorems and Superintegrable Systems”, Regul. Chaotic Dyn., 14:3 (2009), 389–406
Citation in format AMSBIB
\Bibitem{Tsi09}
\by A. V. Tsiganov
\paper Leonard Euler: Addition Theorems and Superintegrable Systems
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 3
\pages 389--406
\mathnet{http://mi.mathnet.ru/rcd588}
\crossref{https://doi.org/10.1134/S1560354709030034}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2525620}
\zmath{https://zbmath.org/?q=an:1229.70055}
Linking options:
  • https://www.mathnet.ru/eng/rcd588
  • https://www.mathnet.ru/eng/rcd/v14/i3/p389
  • This publication is cited in the following 19 articles:
    1. A. V. Tsiganov, “On rotation invariant integrable systems”, Izv. Math., 88:2 (2024), 389–409  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Akash Sinha, Aritra Ghosh, “Jacobi last multiplier and two-dimensional superintegrable oscillators”, Pramana - J Phys, 98:3 (2024)  crossref
    3. Andrey V. Tsiganov, “Rotations and Integrability”, Regul. Chaotic Dyn., 29:6 (2024), 913–930  mathnet  crossref
    4. Crespo F., Rebollo-Perdomo S., Zapata J.L., “Addition Theorems For C-K Real Functions and Applications in Ordinary Differential Equations”, Aequ. Math., 96:2 (2022), 431–452  crossref  mathscinet  isi  scopus
    5. Tsiganov V A., “Discretization and Superintegrability All Rolled Into One”, Nonlinearity, 33:9 (2020), 4924–4939  crossref  mathscinet  zmath  isi  scopus
    6. Vollmer A., “Projectively Equivalent 2-Dimensional Superintegrable Systems With Projective Symmetries”, J. Phys. A-Math. Theor., 53:9 (2020), 095202  crossref  mathscinet  isi  scopus
    7. Tsiganov A.V., “Superintegrable Systems and Riemann-Roch Theorem”, J. Math. Phys., 61:1 (2020), 012701  crossref  mathscinet  zmath  isi  scopus
    8. Andrey V. Tsiganov, “The Kepler Problem: Polynomial Algebra of Nonpolynomial First Integrals”, Regul. Chaotic Dyn., 24:4 (2019), 353–369  mathnet  crossref  mathscinet
    9. Tsiganov A.V., “Elliptic Curve Arithmetic and Superintegrable Systems”, Phys. Scr., 94:8 (2019), 085207  crossref  isi  scopus
    10. Tsiganov A.V., “Transformation of the Stackel Marices Preserving Superintegrability”, J. Math. Phys., 60:4 (2019), 042701  crossref  mathscinet  zmath  isi  scopus
    11. A. V. Tsiganov, “Superintegrable systems with algebraic and rational integrals of motion”, Theoret. and Math. Phys., 199:2 (2019), 659–674  mathnet  mathnet  crossref  crossref  isi  scopus
    12. Yu.A. Grigoriev, A.V. Tsiganov, “On superintegrable systems separable in Cartesian coordinates”, Physics Letters A, 382:32 (2018), 2092  crossref
    13. Andrey V. Tsiganov, “Superintegrable Stäckel systems on the plane: elliptic and parabolic coordinates”, SIGMA, 8 (2012), 031, 9 pp.  mathnet  crossref  mathscinet
    14. Ernie G. Kalnins, Willard Miller Jr., “Structure theory for extended Kepler–Coulomb 3D classical superintegrable systems”, SIGMA, 8 (2012), 034, 25 pp.  mathnet  crossref  mathscinet
    15. Claudia Chanu, Luca Degiovanni, Giovanni Rastelli, “First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator”, SIGMA, 7 (2011), 038, 12 pp.  mathnet  crossref  mathscinet
    16. Claudia Chanu, Luca Degiovanni, Giovanni Rastelli, “Three and Four-body Systems in One Dimension: Integrability, Superintegrability and Discrete Symmetries”, Regul. Chaotic Dyn., 16:5 (2011), 496–503  mathnet  crossref
    17. A.J. Maciejewski, M. Przybylska, A.V. Tsiganov, “On algebraic construction of certain integrable and super-integrable systems”, Physica D: Nonlinear Phenomena, 240:18 (2011), 1426  crossref
    18. A V Tsiganov, “On the superintegrable Richelot systems”, J. Phys. A: Math. Theor., 43:5 (2010), 055201  crossref
    19. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Superintegrable system on a sphere with the integral of higher degree”, Regul. Chaotic Dyn., 14:6 (2009), 615–620  mathnet  crossref
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