Geodesic
The existence of the exact symmetric solutions in the plane Newton problem of many bodies
Matematičeskoe modelirovanie, Tome 10 (1998) no. 8, pp. 74-80.

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The existence of a new class of the exact symmetric solutions is proved for differential equations of movement in the plane Newton problem of $n+1$ bodies, vectorially represented by correct, scale-similarly to self varied polygon, rotated with variable angular speed around the centre $P_0$. 
@article{MM_1998_10_8_a6,
     author = {E. A. Grebenikov},
     title = {The existence of the exact symmetric solutions in the plane {Newton} problem of many bodies},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {74--80},
     publisher = {mathdoc},
     volume = {10},
     number = {8},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1998_10_8_a6/}
}
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E. A. Grebenikov. The existence of the exact symmetric solutions in the plane Newton problem of many bodies. Matematičeskoe modelirovanie, Tome 10 (1998) no. 8, pp. 74-80. http://geodesic.mathdoc.fr/item/MM_1998_10_8_a6/