Unimodal mappings and Li--Yorke chaos
Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 679-689.

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Conditions for unimodal mappings to have domains with a Li–Yorke chaotic behavior of trajectories are found.
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V. A. Dobrynskii. Unimodal mappings and Li--Yorke chaos. Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 679-689. http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a5/

[1] Dobrynskii V. A., “Kriticheskie mnozhestva i unimodalnye otobrazheniya kvadrata”, Dokl. RAN, 341:4 (1995), 442–445 | MR | Zbl

[2] Dobrynskii V. A., “Kriticheskie mnozhestva i unimodalnye otobrazheniya kvadrata”, Matem. zametki, 58:5 (1995), 669–680 | MR | Zbl

[3] Li T.-Y., Yorke J. A., “Period three imply chaos”, Amer. Math. Monthly, 82 (1975), 985–992 | DOI | MR | Zbl

[4] Marotto F. R., “Snap-back repellers imply chaos in $\mathbb R^n$”, J. Math. Anal. Appl., 63:1 (1978), 199–223 | DOI | MR | Zbl

[5] Gumowski I., Mira C., Dynamique Chaotique. Transformations Ponctuelles. Transition Ordre–Désordre, Editions Cepadues, Toulouse, 1980 | Zbl

[6] Dobrynskii V. A., Svoistva tsiklov otobrazhenii, porozhdaemykh raznostnymi uravneniyami vtorogo poryadka s nelineinostyu tipa proizvedenie, Preprint, IM NAN Ukrainy, Kiev, 1994

[7] Hale J. K., Lin X.-B., “Symbolic dynamics and nonlinear semiflows”, Ann. Mat. Pura Appl. (4), 144 (1986), 229–259 | DOI | MR | Zbl

[8] Robinson C., Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, CRC Press, London–Tokyo, 1995