Abstract
A theory is given for the construction of generalized Kustaanheimo—Stiefel (KS) transformations for dimensionsq+1 (q=2 h ,h=0, 1, 2, ...) of the Kepler problem, and the following proposition is proved: A connection between the Kepler problem in a real space of dimensionq+1 and the problem of an isotropic harmonic oscillator in a real space of dimensionN exists and can be established by means of generalized KS transformations in the cases in whichN=2q andq=2 h (h=0, 1, 2, ...). A simple graphical prescription for constructing genralized KS transformations that realize this connection is proposed.
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