The Cantor set as an $\omega$-limit set for iterations of a smooth function on a segment
Matematičeskie zametki, Tome 55 (1994) no. 3, pp. 35-47.

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K. E. Gusev. The Cantor set as an $\omega$-limit set for iterations of a smooth function on a segment. Matematičeskie zametki, Tome 55 (1994) no. 3, pp. 35-47. http://geodesic.mathdoc.fr/item/MZM_1994_55_3_a3/

[1] Bruckner A. M., “The $\omega $-limit sets for self maps of an interval”, Real Anal. Exch., 15:1 (1989–1990), 96–101

[2] McDuff D., “$C^1$-minimal subsets of circle”, Ann. Inst. Fourier. Grenoble, 31:1 (1981), 177–193 | MR | Zbl