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. 
@article{FPM_2016_21_4_a6,
     author = {V. S. Sekovanov},
     title = {Smooth {Julia} sets},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {133--150},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_4_a6/}
}
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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/