Geodesic
Smooth Julia sets
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 4, pp. 133-150.

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It is known that Julia sets, as a rule, have a fractal structure. In this paper, we give examples of smooth Julia sets, among them: a circle, a segment, an infinite interval, a straight line, and the complex plane. It is shown that the functions studied in the paper are chaotic on their Julia sets. The results obtained by analytical research are visualized using computer programs. The algorithms for constructing the Julia sets considered are indicated. 
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V. S. Sekovanov. Smooth Julia sets. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 4, pp. 133-150. http://geodesic.mathdoc.fr/item/FPM_2016_21_4_a6/

[1] Grinchenko V. T., Matsypura V. T., Snarskii A. A., Vvedenie v nelineinuyu dinamiku: Khaos i fraktaly, Izd-vo LKI, M., 2007

[2] Kronover R. M., Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii, Postmarket, M., 2000

[3] Lyubich M. Yu., “Dinamika ratsionalnykh preobrazovanii. Topologicheskaya kartina”, UMN, 41:4 (250) (1986), 35–95 | MR

[4] Milnor Dzh., Golomorfnaya dinamika, RKhD, Izhevsk, 2000

[5] Obuchenie fraktalnoi geometrii i informatike v vuze i shkole v svete idei akademika A. N. Kolmogorova, Mater. mezhdunar. nauch.-metod. konf., KGU, Kostroma, 2016

[6] Paitgen Kh. O., Rikhter P. Kh., Krasota fraktalov. Obrazy kompleksnykh dinamicheskikh sistem, Mir, M., 1993

[7] Sekovanov V. S., “O mnozhestvakh Zhyulia nekotorykh ratsionalnykh funktsii”, Vestn. KGU im. N. A. Nekrasova, 18:2 (2012), 23–28

[8] Sekovanov V. S., Elementy teorii fraktalnykh mnozhestv, Uch. posob., Librokom, M., 2014

[9] Sekovanov V. S., Chto takoe fraktalnaya geometriya?, Lenand, M., 2016

[10] Sekovanov V. S., Elementy teorii diskretnykh dinamicheskikh sistem, Lan, SPb., 2017

[11] Sekovanov V. S., Ivkov V. A., “Mnogoetapnoe matematiko-informatsionnoe zadanie «Strannye attraktory»”, Vestn. KGU, 19:5 (2013), 155–157

[12] Falconer K., Fractal Geometry: Mathematical Foundations and Applications, Wiley, New York, 1990 | MR