Abstract
In this paper we consider superintegrable systems which are an immediate generalization of the Kepler and Hook problems, both in two-dimensional spaces — the plane ℝ2 and the sphere S2 — and in three-dimensional spaces ℝ3 and S3. Using the central projection and the reduction procedure proposed in [21], we show an interrelation between the superintegrable systems found previously and show new ones. In all cases the superintegrals are presented in explicit form.
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