Superintegrability of three-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems

  title={Superintegrability of three-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems},
  author={Jos{\'e} F. Cari{\~n}ena and Manuel F Ra{\~n}ada and Mariano Santander},
  journal={Journal of Physics A: Mathematical and Theoretical},
We study four particular three-dimensional natural Hamiltonian systems defined in conformally Euclidean spaces. We prove their superintegrability and we obtain, in the four cases, the maximal number of functionally independent integrals of motion. The two first systems are related to the three-dimensional isotropic oscillator and the superintegrability is quadratic. The third system is obtained as a continuous deformation of an oscillator with ratio of frequencies 1:1:2 and with three… 
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