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Bruckner, Andrew M. ; Smítal, Jaroslav
The structure of $\omega$-limit sets for continuous maps of the interval. (English). Mathematica Bohemica, vol. 117 (1992), issue 1, pp. 42-47
MSC: 26A18, 37C70, 54H20, 58F12 | MR 1154053 | Zbl 0762.26003 | DOI: 10.21136/MB.1992.126240
Keywords:
discrete dynamical system; continuous map; $\omega$-limit set; homoclinic set
Summary:
We prove that every infinite nowhere dense compact subset of the interval $I$ is an $\omega$-limit set of homoclinic type for a continuous function from $I$ to $I$.
References:
[1] S. J. Agronsky A. M. Bruckner J. G. Ceder T. L. Pearson: The structure of $\omega$-limit sets for continuous functions. Real Analysis Exchange 15 (1989-1990), 483-510. DOI 10.2307/44152033 | MR 1059418
[2] A. N. Šarkovskii: Attracting and attracted sets. Soviet Math. Dokl. 6 (1965), 268-270.
[3] A. N. Šarkovskii: The partially ordered system of attracting sets. Soviet Math. Dokl. 7 (1966), 1384-1386. MR 0209413
[4] A. N. Šarkovskii: Attracting sets containing no cycles. Ukrain. Mat. Ž. 20 (1968), 136-142. (In Russian.) MR 0225314
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