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We propose new construction of the polynomial integrals of motion related to the addition theorems.
Elliptische Funktionen und algebraische Zahlen
H. Weber, · 1908
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Sur l’intégration logique des équations de la dynamique à deux variables: Forces conservatives. Intêgrales cubiques. Mouvements dans le plan
J. Drach · 1935
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Construction of new integrable Hamiltonians in two degrees of freedom
C.R. Holt, · 1982
Earlier work this paper cites.
Superintegrable n = 2 n=2 systems, quadratic constants of motion, and potentials of Drach
M.F.Rañada, · 1997
Earlier work this paper cites.
The Stäckel systems and algebraic curves
A.V. Tsiganov, · 1999
Earlier work this paper cites.
Duality between integrable Stäckel systems
A.V. Tsiganov, · 1999
Cited alongside, same era.
On the Drach superintegrable systems
A.V. Tsiganov, · 2000
Cited alongside, same era.
Complex Euclidean super-integrable potentials, potentials of Drach, and potential of Holt
M.F. Ranada, M. Santander, · 2001
Cited alongside, same era.
The Maupertuis principle and canonical transformations of the extended phase space
A.V. Tsiganov, · 2001
Cited alongside, same era.
Symbolic software for separation of variables in the Hamilton-Jacobi equation for the L-systems
Yu.A. Grigoryev, A.V. Tsiganov, · 2005
Cited alongside, same era.
P. Stäckel, Uber die Integration der Hamilton–Jacobischen Differential Gleichung Mittelst Separation der Variabel
Cited in the paper.
Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two-dimensional manifold
C. Daskaloyannis, K. Ypsilantis, · 2006
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I. Marquette, P. Winternitz, · 2007
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Global action-angle variables for the periodic Toda lattice
A. Henrici, T. Kappeler, · 2008
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On maximally superintegrable systems
A.V. Tsiganov, · 2008
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