Superintegrable deformations of superintegrable systems: quadratic superintegrability and higher-order superintegrability. (English) Zbl 1317.70011
Summary: The superintegrability of four Hamiltonians \(\widetilde{H}_r =\lambda H_r,\; r = a, b, c, d\), where \(H_{r}\) are known Hamiltonians and \(\lambda\) is a certain function defined on the configuration space and depending on a parameter \(\kappa\), is studied. The new Hamiltonians, and the associated constants of motion \(J_{ri}\;, i = 1, 2, 3\), are continuous functions of the parameter \(\kappa\). The first part is concerned with separability and quadratic superintegrability (the integrals of motion are quadratic in the momenta) and the second part is devoted to the existence of higher-order superintegrability. The results obtained in the second part are related with the Tremblay-Turbiner-Winternitz and the Post-Winternitz systems.{
©2015 American Institute of Physics}
©2015 American Institute of Physics}
MSC:
| 70H05 | Hamilton’s equations |
| 70H06 | Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics |
| 70H33 | Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics |
| 37N05 | Dynamical systems in classical and celestial mechanics |
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