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ISSN : 1226-0657

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Vol.5 No.1

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A NOTE ON MINIMAL SETS OF THE CIRCLE MAPS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1998, v.5 no.1, pp.13-16
Yang, Seung-Kab (Department of Mathematics, MyongJi University)
Min, Kyung-Jin (Department of Mathematics, MyongJi University)
Yang, Seung-Kab, & Min, Kyung-Jin. (1998). A NOTE ON MINIMAL SETS OF THE CIRCLE MAPS. 한국수학교육학회지시리즈B:순수및응용수학, 5(1), 13-16.

Abstract

For continuous maps f of the circle to itself, we show that (1) every <TEX>$\omega$</TEX>-limit point is recurrent (or almost periodic) if and only if every <TEX>$\omega$</TEX>-limit set is minimal, (2) every <TEX>$\omega$</TEX>-limit set is almost periodic, then every <TEX>$\omega$</TEX>-limit set contains only one minimal set.

keywords
Recurrent set, almost periodic set, <tex> $\omega$</tex>-limit set, minimal set

한국수학교육학회지시리즈B:순수및응용수학

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