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2009

Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere

Bellucci, Stefano, Toppan, Francesco, Yeghikyan, Vahagn

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Using the second Hopf map, we perform the reduction of the eight-dimensional (pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting with a Yang monopole.

Then, using a standard trick, we obtain, from the latter system, the pseudospherical and spherical generalizations of the Yang-Coulomb system (the five dimensional analog of MICZ-Kepler system).
We present the whole set of its constants of motions, including the hidden symmetry generators given by the analog of Runge-Lenz vector.
In the same way, starting from the eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the integrable (pseudo)spherical generalization of the Yang-Coulomb system with the Stark term.

Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere · Around

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