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We consider the Euler approach to construction and to investigation of the superintegrable systems related to the addition theorems.
On hyperelliptic f unctions of genus two
A.L. Dixon, · 1932
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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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L. Euler, Institutiones Calculi integralis, Ac.Sc. Petropoli, 1761, (Russian translation GITL, Moskow, 1956.)
1956
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Finitely many mass points on the line under the influence of an exponential potential - an integrable system
J. Moser, · 1975
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Intrinsic characterization of the variable separation in the Hamilton-Jacobi equation
S. Benenti, · 1997
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The Stäckel systems and algebraic curves
A.V. Tsiganov, · 1999
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Duality between integrable Stäckel systems
A.V. Tsiganov, · 1999
Cited alongside, same era.
A. Ibort, F. Magri, G. Marmo, Bihamiltonian structures and Stäckel separability
2000
Cited alongside, same era.
On the Drach superintegrable systems
A.V. Tsiganov, · 2000
Cited alongside, same era.
Completeness of superintegrability in two-dimensional constant-curvature spaces
E.G. Kalnins, J.M. Kress, G.S. Pogosyan and W. Miller, · 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.
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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Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties
E.G. Kalnins, J.M. Kress, W. Miller Jr, · 2007
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Global action-angle variables for the periodic Toda lattice
A. Henrici, T. Kappeler, · 2008
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Superintegrable systems with third-order integrals of motion
I. Marquette, P. Winternitz, · 2008
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On maximally superintegrable systems
A.V. Tsiganov, · 2008
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Addition theorem and the Drach superintegrable systems
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Theory of Equations
W.S. Burnside and A.W. Panton,
Cited in the paper.
An Elementary Treatise on Elliptic Functions
A. Cayley,
Cited in the paper.
G. Darboux, Leçons sur la Théorie Générale des Surfaces, 1898
Cited in the paper.
On the Euler superintegrable systems
Yu A Grigoryev, V. A. Khudobakhshov, A V Tsiganov,
Cited in the paper.
Sur les géodésiques a intégrales quadratiques
M.G. Koenigs,
Cited in the paper.
Ueber die Integration eines merkwürdigen Systems von Differentialgleichungen
F. Richelot,
Cited in the paper.
A.V. Tsiganov, · 2008
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