{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T15:02:43Z","timestamp":1770562963576,"version":"3.49.0"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,8]]},"abstract":"<jats:p> Let [Formula: see text] be a local dendrite and let [Formula: see text] be a monotone map. Denote by [Formula: see text], RR[Formula: see text], UR[Formula: see text], [Formula: see text] the set of periodic (resp., regularly recurrent, uniformly recurrent, recurrent) points and [Formula: see text] the union of all [Formula: see text]-limit sets of [Formula: see text]. We show that if [Formula: see text] is nonempty, then (i) [Formula: see text]. (ii) R[Formula: see text] if and only if every cut point is a periodic point. If [Formula: see text] is empty, then (iii) [Formula: see text]. (iv) R[Formula: see text] if and only if [Formula: see text] is a circle and [Formula: see text] is topologically conjugate to an irrational rotation of the unit circle [Formula: see text]. On the other hand, we prove that [Formula: see text] has no Li\u2013Yorke pair. Moreover, we show that the family of all [Formula: see text]-limit sets of [Formula: see text] is closed with respect to the Hausdorff metric. <\/jats:p>","DOI":"10.1142\/s0218127416501509","type":"journal-article","created":{"date-parts":[[2016,8,30]],"date-time":"2016-08-30T05:32:56Z","timestamp":1472535176000},"page":"1650150","source":"Crossref","is-referenced-by-count":12,"title":["Invariant Sets for Monotone Local Dendrite Maps"],"prefix":"10.1142","volume":"26","author":[{"given":"Hafedh","family":"Abdelli","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Jarzouna 7021, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Habib","family":"Marzougui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Jarzouna 7021, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,8,30]]},"reference":[{"key":"S0218127416501509BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2014.12.003"},{"key":"S0218127416501509BIB002","author":"Abouda H.","year":"2015","journal-title":"Topol. Appl."},{"key":"S0218127416501509BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.089"},{"key":"S0218127416501509BIB004","doi-asserted-by":"publisher","DOI":"10.1515\/crll.2002.053"},{"key":"S0218127416501509BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084762"},{"key":"S0218127416501509BIB006","first-page":"2087","volume":"139","author":"Hattab H.","year":"2011","journal-title":"Proc. Amer. Math. Soc."},{"key":"S0218127416501509BIB007","series-title":"Monogr. Pure Appl. Math.","volume-title":"Hyperspaces; Fundamentals and Recent Advances","volume":"216","author":"Illanes A.","year":"1999"},{"key":"S0218127416501509BIB008","volume-title":"Topology","volume":"2","author":"Kuratowski K.","year":"1968"},{"key":"S0218127416501509BIB009","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385704000720"},{"key":"S0218127416501509BIB010","doi-asserted-by":"publisher","DOI":"10.4064\/fm196-1-2"},{"key":"S0218127416501509BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2007.03.008"},{"key":"S0218127416501509BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740902372X"},{"key":"S0218127416501509BIB013","doi-asserted-by":"publisher","DOI":"10.1201\/9781315274089"},{"key":"S0218127416501509BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411030465"},{"key":"S0218127416501509BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2011.08.020"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416501509","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:42:45Z","timestamp":1565080965000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416501509"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8]]},"references-count":15,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2016,8,30]]},"published-print":{"date-parts":[[2016,8]]}},"alternative-id":["10.1142\/S0218127416501509"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416501509","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,8]]}}}