Geodesic
Rate of convergence in the “circle formation” problem
Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 89-118 
A. M. Leontovich. Rate of convergence in the “circle formation” problem. Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 89-118. http://geodesic.mathdoc.fr/item/SM_1972_17_1_a4/
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     title = {Rate of convergence in the {\textquotedblleft}circle formation{\textquotedblright} problem},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_17_1_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider transformations obtained from local homogeneous rules of motion of polygons in the plane for which regular polygons are stationary (the so-called “circle formation” problem). These transformations are studied for initial states that are close to regular polygons. A method of determination of the rate of convergence to regular polygons is presented; on this basis we obtain estimates of the highest rate of convergence. Figures: 1. Bibliography: 4 titles.

[1] A. M. Leontovich, I. I. Pyatetskii-Shapiro, O. N. Stavskaya, “Zadacha okruzhivaniya v matematicheskoi modeli formoobrazovaniya”, Avtomatika i telemekhanika, 1971, no. 2, 100–110 | MR | Zbl

[2] S. Smeil, “Differentsiruemye dinamicheskie sistemy”, Uspekhi matem. nauk, XXV:1(151) (1970), 113–185 | MR

[3] F. Khartman, Obyknovennye differentsialnye uravneniya (glava IX), Mir, Moskva, 1970 | MR | Zbl

[4] A. M. Leontovich, I. I. Pyatetskii-Shapiro, O. N. Stavskaya, “Nekotorye matematicheskie zadachi, svyazannye s formoobrazovaniem”, Avtomatika i telemekhanika, 1970, no. 4, 94–107 | MR | Zbl