Geodesic
Limit sets for maps of the circle
Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 736-742 
V. V. Redkozubov. Limit sets for maps of the circle. Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 736-742. http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a9/
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     title = {Limit sets for maps of the circle},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A trick which reduces some questions concerning the dynamics of self-maps of the circle to similar questions about self-maps of the interval is suggested and applied to answer two questions of Block and Coppel.

[1] Block L. S., Coppel W. A., Dynamics in One Dimension, Springer-Verlag, N.Y., 1992 | MR

[2] Block L., Coven E., Mulvey I., Nitecki Z., “Homoclinic and nonwandering points for maps of the circle”, Ergod. Theor. Dynam. Sist., 3 (1983), 521–532 | MR | Zbl

[3] Llibre J., Misiurewicz M., “Horseshoes, entropy and periods for graph maps”, Topology, 32:3 (1993), 649–664 | DOI | MR | Zbl

[4] Auslander J., Katznelson Y., “Continuous maps of the circle without periodic points”, Israel. J. Math., 32 (1979), 375–381 | DOI | MR | Zbl

[5] Bae J., Yang K., “$\omega$-limit sets for maps of the circle”, Bull. Korean Math. Soc., 25 (1988), 233–242 | MR | Zbl

[6] Evans M., Humke P., Lee Ch., O'Malley R., “Characterizations of turbulent one-dimensional mappings via $\omega$-limit sets”, Trans. Amer. Math. Soc., 326:1 (1991), 261–280 | DOI | MR | Zbl

[7] Blokh A. M., “O dinamicheskikh sistemakh na odnomernykh razvetvlennykh mnogoobraziyakh. 1; 2; 3”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 46 (1986), 8–18 ; 47 (1986), 67–77; 48 (1987), 32–46 | Zbl