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Master integrals, superintegrability and quadratic algebras. (English) Zbl 1010.37033
Summary: We use a generalization of Oevel’s theorem about master symmetries to relate them with superintegrability and quadratic algebras.

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
Full Text: DOI
[1] Calogero, F., Motion of poles and zeros of nonlinear and linear partial differential equations and related many-body problems, Nuovo cimento, 43B, 177-241, (1978)
[2] Caseiro, R.; Françoise, J.-P., Algebraically linearizable dynamical systems, preprint dept. matemática da universidade de Coimbra, 99/10
[3] Caseiro, R.; Françoise, J.-P.; Sasaki, R., Algebraic linearization of dynamics of Calogero type for any Coxeter group, J. math. phys., 41, 4679-4986, (2000) · Zbl 0985.37061
[4] Caseiro, R.; Françoise, J.-P.; Sasaki, R., Quadratic algebra associated with rational Calogero-Moser models, J. math. phys., 42, 5321-5340, (2001) · Zbl 1018.81022
[5] Fernandes, R., Completely integrable bi-Hamiltonian systems, J. dynamics differential equations, 6, 53-69, (1994) · Zbl 0796.58020
[6] Kuznetsov, V., Hidden symmetry of the quantum Calogero-Moser system, Phys. lett. A, 218, 212-222, (1996) · Zbl 0972.39503
[7] Magri, F., A simple model of the integrable Hamiltonian equation, J. math. phys., 19, 5, 1156-1162, (1978) · Zbl 0383.35065
[8] F. Magri, C. Morosi, A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson-Nijenhuis manifolds, Quaderno S19, Universiá di Milano, 1984
[9] Morosi, C.; Tondo, G., On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian, Phys. lett. A, 247, 59-64, (1998) · Zbl 1044.37536
[10] Oevel, W., A geometrical approach to integrable systems admitting time dependent invariants, (), 108-124 · Zbl 0736.35119
[11] Rañada, M., Superintegrability of the rational Calogero-Moser system: constants of motion, master symmetries and time-dependent symmetries, J. math. phys., 40, 1, 236-247, (1999) · Zbl 0956.37041
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