Geodesic
From Averaging to Statistical Physics
Informatics and Automation, Problems of the modern mathematical physics, Tome 228 (2000), pp. 196-202.

Voir la notice de l'article provenant de la source Math-Net.Ru

N. N. Bogolyubov's averaging method for dynamical systems with fast and slow variables as well as its applications and analogues in various branches of science are discussed. 
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V. I. Arnol'd. From Averaging to Statistical Physics. Informatics and Automation, Problems of the modern mathematical physics, Tome 228 (2000), pp. 196-202. http://geodesic.mathdoc.fr/item/TRSPY_2000_228_a14/

[1] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh uravnenii, 2-e izd., Izd-vo AN SSSR, M., 1958, 408 pp. | MR

[2] Poincaré H., Les méthodes nouvelles de la mécanique céleste, v. 1, Gauthier-Villars, Paris, 1892 ; v. 2, 1893; v. 3, 1899 | Zbl

[3] Lindstedt A., “Beitrag zur Integration der Differentialgleichungen der Störungstheorie”, Mém. Acad. imp. sci. St.-Pétersbourg, 31:4 (1883)

[4] Arnold V. I., “Ob ustoichivosti polozheniya ravnovesiya gamiltonovoi sistemy”, DAN SSSR, 138:1 (1961), 13–15 | MR

[5] Charlier C. L., Die Mechanik des Himmels, 2 aufl., Bd. 1, W. de Gruyter, Berlin, 1927, VII+488 S. ; Bd. 2, VIII+478 S | Zbl

[6] Lidov M. L., “O priblizhennom analize evolyutsii orbit iskusstvennykh sputnikov”, Problemy dvizheniya iskusstvennykh nebesnykh tel, Izd-vo AN SSSR, M., 1963, 119–134

[7] Anosov D. V., “Osrednenie v sistemakh obyknovennykh differentsialnykh uravnenii s bystro koleblyuschimisya resheniyami”, Izv. AN SSSR. Ser. mat., 24:5 (1960), 721–742 | MR | Zbl

[8] Neishtadt A. I., “Averaging of perturbations”, Dynamical Systems – III, Encycl. Math. Sci., 3, ed. V. I. Arnold, Springer-Verlag, Berlin etc., 1988, Ch. 5, 138–167 ; World Publ. Corp., Beijing, 1989 | MR

[9] Arnold V. I., “O povedenii adiabaticheskogo invarianta pri medlennom periodicheskom izmenenii funktsii Gamiltona”, DAN SSSR, 142:4 (1962), 758–761 | MR

[10] Newcomb S., “Note on the frequency of use of different digits in natural numbers”, Amer. J. Math., 4 (1881), 39–40 | DOI | MR

[11] Benford F., “The law of anomalous numbers”, Proc. Amer. Phil. Soc., 78 (1938), 557–572