{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T09:06:39Z","timestamp":1775120799393,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,3]]},"abstract":"<jats:p> Two-dimensional (Z<jats:sub>1<\/jats:sub>\u2013Z<jats:sub>3<\/jats:sub>\u2013Z<jats:sub>1<\/jats:sub>) maps are such that the plane is divided into three unbounded open regions: a region Z<jats:sub>3<\/jats:sub>, whose points generate three real rank-one preimages, bordered by two regions Z<jats:sub>1<\/jats:sub>, whose points generate only one real rank-one preimage. This paper is essentially devoted to the study of the structures, and the global bifurcations, of the basins of attraction generated by such maps. In particular, the cases of fractal structure of such basins are considered. For the class of maps considered in this paper, a large variety of dynamic situations is shown, and the bifurcations leading to their occurrence are explained. <\/jats:p>","DOI":"10.1142\/s0218127406015039","type":"journal-article","created":{"date-parts":[[2006,5,23]],"date-time":"2006-05-23T11:19:24Z","timestamp":1148383164000},"page":"647-669","source":"Crossref","is-referenced-by-count":9,"title":["BASIN FRACTALIZATIONS GENERATED BY A TWO-DIMENSIONAL FAMILY OF (Z<sub>1<\/sub>\u2013Z<sub>3<\/sub>\u2013Z<sub>1<\/sub>) MAPS"],"prefix":"10.1142","volume":"16","author":[{"given":"GIAN-ITALO","family":"BISCHI","sequence":"first","affiliation":[{"name":"Istituto di Scienze Economiche, University of Urbino, Italy"}]},{"given":"LAURA","family":"GARDINI","sequence":"additional","affiliation":[{"name":"Istituto di Scienze Economiche, University of Urbino, Italy"}]},{"given":"CHRISTIAN","family":"MIRA","sequence":"additional","affiliation":[{"name":"CESNLA 19 rue d'Occitanie, Fonsegrives, 31130 QUINT, and Istituto di Scienze Economiche, University of Urbino, Italy"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499000079"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403007096"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497000972"},{"key":"rf4","volume-title":"Dynamique Chaotique","author":"Gumowski I.","year":"1980"},{"key":"rf5","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0089135","volume-title":"Recurrences and Discrete Dynamic Systems","volume":"809","author":"Gumowski I.","year":"1980"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497000042"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/0413"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127494000241"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/9789812798732"},{"key":"rf10","first-page":"1439","volume":"6","author":"Mira C.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403007631"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497001527"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127406015039","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:10:11Z","timestamp":1565136611000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127406015039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3]]},"references-count":12,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,3]]}},"alternative-id":["10.1142\/S0218127406015039"],"URL":"https:\/\/doi.org\/10.1142\/s0218127406015039","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3]]}}}