{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:56:46Z","timestamp":1772290606931,"version":"3.50.1"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2000,6]]},"abstract":"<jats:p> In this paper we show that unbounded chaotic trajectories are easily observed in the iteration of maps which are not defined everywhere, due to the presence of a denominator which vanishes in a zero-measure set. Through simple examples, obtained by the iteration of one-dimensional and two-dimensional maps with denominator, the basic mechanisms which are at the basis of the existence of unbounded chaotic trajectories are explained. Moreover, new kinds of contact bifurcations, which mark the transition from bounded to unbounded sets of attraction, are studied both through the examples and by general theoretical methods. Some of the maps studied in this paper have been obtained by a method based on the Schr\u00f6oder functional equation, which allows one to write closed analytical expressions of the unbounded chaotic trajectories, in terms of elementary functions. <\/jats:p>","DOI":"10.1142\/s0218127400000980","type":"journal-article","created":{"date-parts":[[2003,5,22]],"date-time":"2003-05-22T02:35:01Z","timestamp":1053570901000},"page":"1437-1469","source":"Crossref","is-referenced-by-count":15,"title":["UNBOUNDED SETS OF ATTRACTION"],"prefix":"10.1142","volume":"10","author":[{"given":"GIAN-ITALO","family":"BISCHI","sequence":"first","affiliation":[{"name":"Istituto di Scienze Economiche, University of Urbino,  61029 Urbino, Italy"}]},{"given":"CHRISTIAN","family":"MIRA","sequence":"additional","affiliation":[{"name":"19 rue d'Occitanie, Fonsegrives 31130 Quint,  MIDIVAL, 2 rue Camichel, 31071 Toulouse Cedex, France"}]},{"given":"LAURA","family":"GARDINI","sequence":"additional","affiliation":[{"name":"Istituto di Matematica \"Levi\", University of Parma, Italy"},{"name":"Istituto di Scienze Economiche, University of  Urbino 61029 Urbino, Italy"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.166158"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.79.1018"},{"key":"p_4","first-page":"44","volume":"121","author":"Billings L.","year":"1998","journal-title":"Physica"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497001229"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499000079"},{"key":"p_7","first-page":"91","volume":"13","author":"Bischi G. I.","year":"1999","journal-title":"Annales Mathematical Silesianae"},{"issue":"3","key":"p_8","first-page":"143","volume":"26","author":"Bischi G. I.","year":"1997","journal-title":"Economic Notes"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496000023"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211162"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1063\/1.166414"},{"key":"p_13","first-page":"1","author":"Latt\u00e8s S.","year":"1906","journal-title":"Annali di Matematica, Serie III, Tomo"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211121"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496000850"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127494001210"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127400000980","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:44:09Z","timestamp":1565109849000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127400000980"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,6]]},"references-count":14,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2000,6]]}},"alternative-id":["10.1142\/S0218127400000980"],"URL":"https:\/\/doi.org\/10.1142\/s0218127400000980","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,6]]}}}