Geodesic
A method of the dissipative Henon map renormalization
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1893-1908 
Yu. V. Bibik; D. A. Sarancha. A method of the dissipative Henon map renormalization. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1893-1908. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a2/
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     author = {Yu. V. Bibik and D. A. Sarancha},
     title = {A method of the dissipative {Henon} map renormalization},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A mechanism for period doubling and transition to chaos for the dissipative Henon map is investigated. The renormalization group technique is used for that purpose. In the context of this technique, a special approach is developed that relates the renormalization procedure with the simpler problem of the renormalization of the conservative Henon map.

[1] Sinai Ya. G., Shilnikov L. P. (red.), Strannye attraktory, Mir, M., 1981 | MR

[2] Tabor M., Khaos i integriruemost v nelineinoi dinamike, Editorial URSS, M., 2001

[3] Li T. Y., Yorke J. A., “Period three implies chaos”, Amer. Math. Monthly, 82 (1975), 985–992 | DOI | MR

[4] Shuster G., Determinirovannyi khaos, Mir, M., 1988 | MR | Zbl

[5] Hellemann R. H. G., “Self-generated chaotic behaviour in nonlinear mechanics”, Fundamental Problems in Statistical Mechanics, 5, North-Holland Publ., Amsterdam, 1980 | MR

[6] Mackay R. S., Renormalization in area-preserving maps, Ph. D. Thesis, Princeton Univ.; Univ. Microfilms Inc., Ann Arbor, MI, 1982 | MR

[7] Volterra V., Matematicheskaya teoriya borby za suschestvovanie, Nauka, M., 1976 | MR

[8] Bazykin A. D., Nelineinaya dinamika vzaimodeistvuyuschikh populyatsii, In-t kompyuternykh issl., Moskva–Izhevsk, 2003

[9] Prasolov V. V., Solovev Yu. P., Ellipticheskie krivye i algebraicheskie uravneniya, Faktorial, M., 1997