Abstract:
Locally any completely integrable system is maximally superintegrable system since we have the necessary number of the action-angle variables. The main problem is the construction of the single-valued additional integrals of motion on the whole phase space by using these multi-valued action-angle variables. Some constructions of the additional integrals of motion for the Stackel systems and for the integrable systems related with two different quadratic r-matrix algebras are discussed. Among these system there are the open Heisenberg magnet and the open Toda lattices associated with the different root systems.
Keywords:
superintegrable systems, Toda lattices, Stackel systems.
This publication is cited in the following 27 articles:
A. V. Tsyganov, “O tenzornykh invariantakh dlya integriruemykh sluchaev dvizheniya tverdogo tela Eilera, Lagranzha i Kovalevskoi”, Izv. RAN. Ser. matem., 89:2 (2025), 161–188
A. V. Tsiganov, “On rotation invariant integrable systems”, Izv. Math., 88:2 (2024), 389–409
Akash Sinha, Aritra Ghosh, “Jacobi last multiplier and two-dimensional superintegrable oscillators”, Pramana - J Phys, 98:3 (2024)
Andrey V. Tsiganov, “Rotations and Integrability”, Regul. Chaotic Dyn., 29:6 (2024), 913–930
Akash Sinha, Aritra Ghosh, Bijan Bagchi, “Dynamical symmetries of the anisotropic oscillator”, Phys. Scr., 98:9 (2023), 095253
İsmet Yurduşen, Adrián Mauricio Escobar-Ruiz, Irlanda Palma y Meza Montoya, “Doubly Exotic Nth-Order Superintegrable Classical Systems Separating in Cartesian Coordinates”, SIGMA, 18 (2022), 039, 20 pp.
Idriss El Fakkousy, Bouchta Zouhairi, Mohammed Benmalek, Jaouad Kharbach, Abdellah Rezzouk, Mohammed Ouazzani-Jamil, “Classical and quantum integrability of the three-dimensional generalized trapped ion Hamiltonian”, Chaos, Solitons & Fractals, 161 (2022), 112361
Deshmukh P.C., Ganesan A., Banerjee S., Mandal A., “Accidental Degeneracy of the Hydrogen Atom and Its Non-Accidental Solution in Parabolic Coordinates”, Can. J. Phys., 99:10 (2021), 853–860
Lazureanu C., “On the Integrable Deformations of the Maximally Superintegrable Systems”, Symmetry-Basel, 13:6 (2021), 1000
Tsiganov A.V., “Reduction of Divisors For Classical Superintegrable Gl(3) Magnetic Chain”, J. Math. Phys., 61:11 (2020), 112703
Tsiganov A.V., “Superintegrable Systems and Riemann-Roch Theorem”, J. Math. Phys., 61:1 (2020), 012701
Andrey V. Tsiganov, “The Kepler Problem: Polynomial Algebra of Nonpolynomial First Integrals”, Regul. Chaotic Dyn., 24:4 (2019), 353–369
Tsiganov A.V., “Transformation of the Stackel Marices Preserving Superintegrability”, J. Math. Phys., 60:4 (2019), 042701
Yu.A. Grigoriev, A.V. Tsiganov, “On superintegrable systems separable in Cartesian coordinates”, Physics Letters A, 382:32 (2018), 2092
Yuxuan Chen, Ernie G. Kalnins, Qiushi Li, Willard Miller Jr., “Examples of Complete Solvability of 2D Classical Superintegrable Systems”, SIGMA, 11 (2015), 088, 51 pp.
Willard Miller, Sarah Post, Pavel Winternitz, “Classical and quantum superintegrability with applications”, J. Phys. A: Math. Theor., 46:42 (2013), 423001
I. A. Bizyaev, A. V. Tsyganov, “O sfere Rausa”, Nelineinaya dinam., 8:3 (2012), 569–583
Andrey V. Tsiganov, “Superintegrable Stäckel systems on the plane: elliptic and parabolic coordinates”, SIGMA, 8 (2012), 031, 9 pp.
Ernie G. Kalnins, Willard Miller Jr., “Structure theory for extended Kepler–Coulomb 3D classical superintegrable systems”, SIGMA, 8 (2012), 034, 25 pp.
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