A study of iteration of cubic maps with the position of linear conjugacy
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 20-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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The device of a linear conjugacy is applied to research of real cubic maps. The program of studying of map cycles is proposed. This program is connected with construction of multipliers constancy lines on the half-plane of material parameters. We study the cycles of small periods: 1 and 2-cycles, and also – it is less detailed – 3-cycles.
Keywords: cubic mapping, linear conjugacy, the stability region of cycles.
Mots-clés : line multipliers cycles
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V. A. Gustomesov. A study of iteration of cubic maps with the position of linear conjugacy. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 20-39. http://geodesic.mathdoc.fr/item/VUU_2011_1_a3/

[1] Sharkovskii A. N., Kolyada S. F., Sivak A. G., Fedorenko V. V., Dinamika odnomernykh otobrazhenii, Naukova dumka, Kiev, 1989, 216 pp. | MR

[2] Gukenkheimer Dzh., Kholms F., Nelineinye kolebaniya, dinamicheskie sistemy i bifurkatsii vektornykh polei, IKI, Moskva–Izhevsk, 2002, 560 pp.

[3] Shapiro A. P., Luppov A. P., Rekurrentnye uravneniya v populyatsionnoi biologii, Nauka, M., 1982, 131 pp. | MR

[4] Scjolding H., Branner-Jorgensen B., Christiansen P. L., Jensen H. E., “Bifurcations in Discrete Dynamical Systems with Cubic Maps”, SIAM J. Appl. Math., 43:3 (1983), 520–534 | DOI | MR

[5] Kuznetsov A. P., Kuznetsov S. P., Sataev I. R., “Korazmernost i tipichnost v kontekste problemy opisaniya perekhoda k khaosu cherez udvoeniya perioda v dissipativnykh dinamicheskikh sistemakh”, Regulyarnaya i khaoticheskaya dinamika, 2:3–4 (1997), 90–105 | MR | Zbl

[6] Li M.-C., “Point Bifurcations and Bubbles for a Cubic Family”, Journ. Difference Equat. and Appl., 9:6 (2003), 553–558 | DOI | MR | Zbl

[7] Cabral F., Lago A., Gallas J., “A Picture Book of Two Families of Cubic Maps”, International Journal of Modern Physics C, 4:3 (1993), 553–568 | DOI | MR | Zbl

[8] Kuznetsov A. P., “Cherez ekran kompyutera – v mir nelineinoi dinamiki”, Izvestiya vuzov. Prikladnaya nelineinaya dinamika, 6:5 (1998), 89–101

[9] Gustomesov V. A., “Izuchenie iteratsii kvadratichnykh funktsii s pozitsii lineinoi sopryazhënnosti”, Sb. dokl. Vseros. konf., ch. 1, Samar. gos. ped. un-t, Samara, 2007, 92–96

[10] Branner B., Hubbard J. H., “The Iteration of Cubic Polinomials, part 1: The Global Topology of Parameter Space”, Acta Matem., 160 (1988), 143–206 | DOI | MR | Zbl

[11] Branner B., Hubbard J. H., “The Iteration of Cubic Polinomials, part 2: Patterns and Parapatterns”, Acta Matem., 169 (1992), 229–325 | DOI | MR | Zbl

[12] Milnor J., “Remarks on Iterated Cubic Maps”, Experimental Math., 1 (1992), 5–24 | MR | Zbl

[13] Nishizawa K., Nojiri A., “Center Curves in the Moduli Space of the Real Cubic Maps”, Proc. Japan Acad. Ser. A, 69:6 (1993), 179–184 | DOI | MR | Zbl

[14] Gustomesov V. A., “Issledovanie tsiklov kubicheskikh otobrazhenii s pozitsii lineinoi sopryazhënnosti”, Tez. dokl. II Ukrainskogo matematicheskogo kongressa, Kiev, 2009 http://www.imath.kiev.ua/~congress2009/Abstracts/Gustomesov

[15] Gaushus E. V., Issledovanie dinamicheskikh sistem metodom tochechnykh preobrazovanii, Nauka, M., 1976, 368 pp. | MR

[16] Kurosh A. G., Kurs vysshei algebry, Nauka, M., 1968, 350 pp. | MR