Geodesic
Generalized Kustaanheimo--Stiefel transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 1, pp. 75-80

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In this paper the theory of constructing the generalized KS transformations is given for the Kepler problem dimensions $q+1$ ($q=2^h$, $h=0,1,2,\dots$). The following theorem is proved: The connection between the Kepler problem in $(q+1)$-dimensional real space and the problem of an isotropic harmonic oscillator in real space of dimension $N$ exists and can be established by using the generalized KS transformations only for the cases, when $N=2q$ and $q=2^h$ ($h=0,1,2,\dots$). A simple graphic method of constructing the generalized KS transformations realizing this connection is also suggested. 
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     author = {L. I. Komarov and Le Van Hoang},
     title = {Generalized {Kustaanheimo--Stiefel} transformations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {75--80},
     publisher = {mathdoc},
     volume = {99},
     number = {1},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_1_a6/}
}
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L. I. Komarov; Le Van Hoang. Generalized Kustaanheimo--Stiefel transformations. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 1, pp. 75-80. http://geodesic.mathdoc.fr/item/TMF_1994_99_1_a6/