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The union of the limit points of all backward trajectories through [Formula: see text] was called by Hero the \u201cspecial [Formula: see text]-limit\u201d ([Formula: see text]-limit for short) of [Formula: see text]. In this article, we show that there is a hierarchy of [Formula: see text]-limits of points under iterations of a S-unimodal map: the size of the [Formula: see text]-limit of a point increases monotonically as the point gets closer and closer to the attractor. The [Formula: see text]-limit of any point of the attractor is the whole nonwandering set. This hierarchy reflects the structure of the graph of a S-unimodal map recently introduced jointly by Jim Yorke and the present author. <\/jats:p>","DOI":"10.1142\/s0218127422300130","type":"journal-article","created":{"date-parts":[[2022,5,27]],"date-time":"2022-05-27T11:36:12Z","timestamp":1653651372000},"source":"Crossref","is-referenced-by-count":1,"title":["Backward Asymptotics in S-Unimodal Maps"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-3714-6022","authenticated-orcid":false,"given":"Roberto","family":"De Leo","sequence":"first","affiliation":[{"name":"Department of Mathematics, Howard University, 2400 6th St. NW, Washington, DC 20059, USA"}]}],"member":"219","published-online":{"date-parts":[[2022,5,27]]},"reference":[{"key":"S0218127422300130BIB001","doi-asserted-by":"publisher","DOI":"10.4064\/sm8553-7-2016"},{"key":"S0218127422300130BIB002","doi-asserted-by":"publisher","DOI":"10.12785\/amis\/070530"},{"key":"S0218127422300130BIB003","doi-asserted-by":"publisher","DOI":"10.1126\/science.51.1307.51"},{"key":"S0218127422300130BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(75)90065-0"},{"key":"S0218127422300130BIB006","volume-title":"Iterated Maps on the Interval as Dynamical Systems","author":"Collet P.","year":"1980"},{"key":"S0218127422300130BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/038"},{"key":"S0218127422300130BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2009.04.054"},{"key":"S0218127422300130BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X19500993"},{"key":"S0218127422300130BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S021812742030027X"},{"key":"S0218127422300130BIB011","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2021075"},{"key":"S0218127422300130BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-021-06561-6"},{"key":"S0218127422300130BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-78043-1"},{"key":"S0218127422300130BIB014","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1008"},{"key":"S0218127422300130BIB015","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.48.1507"},{"key":"S0218127422300130BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/BF01982351"},{"key":"S0218127422300130BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/BF01205554"},{"key":"S0218127422300130BIB019","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511998188"},{"key":"S0218127422300130BIB020","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740300731X"},{"key":"S0218127422300130BIB021","first-page":"1015","volume":"116","author":"Hero M.","year":"1992","journal-title":"Proc. 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