Degenerate integrable systems on the plane with a cubic integral of motion

DOI10.1007/BF02551000zbMath1009.70020MaRDI QIDQ5941981

Andreĭ Vladimirovich Tsyganov

Publication date: 12 December 2002

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

cubic conservation lawsdegenerate integrable systemsDrach's conservation lawsoscillator-type Hamiltonian

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

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Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two-dimensional manifold ⋮ Discrete symmetries of equations of dynamics with polynomial integrals of higher degrees ⋮ Quantum superintegrable systems with quadratic integrals on a two dimensional manifold ⋮ Bi-Hamiltonian systems of natural form

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