{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T05:51:58Z","timestamp":1723182718957},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,10]]},"abstract":"<jats:p> Part I of this paper has been devoted to properties of the different Julia set configurations, generated by the complex map T<jats:sub>Z<\/jats:sub>: z\u2032 = z<jats:sup>2<\/jats:sup> - c, c being a real parameter, -1\/4 &lt; c &lt; 2. These properties were revisited from a detailed knowledge of the fractal organization (called \"box-within-a-box\"), generated by the map x\u2032 = x<jats:sup>2<\/jats:sup> - c with x a real variable. Here, the second part deals with an embedding of T<jats:sub>Z<\/jats:sub> into the two-dimensional noninvertible map [Formula: see text]; y\u2032 = \u03b3 y + 4x<jats:sup>2<\/jats:sup>y, \u03b3 \u2265 0. For [Formula: see text] is semiconjugate to T<jats:sub>Z<\/jats:sub> in the invariant half plane (y \u2264 0). With a given value of c, and with \u03b3 decreasing, the identification of the global bifurcations sequence when \u03b3 \u2192 0, permits to explain a route toward the Julia sets, from a study of the basin boundary of the attractor located on y = 0. <\/jats:p>","DOI":"10.1142\/s021812740902475x","type":"journal-article","created":{"date-parts":[[2009,12,15]],"date-time":"2009-12-15T06:45:55Z","timestamp":1260859555000},"page":"3235-3282","source":"Crossref","is-referenced-by-count":3,"title":["FROM THE BOX-WITHIN-A-BOX BIFURCATION STRUCTURE TO THE JULIA SET PART II: BIFURCATION ROUTES TO DIFFERENT JULIA SETS FROM AN INDIRECT EMBEDDING OF A QUADRATIC COMPLEX MAP"],"prefix":"10.1142","volume":"19","author":[{"given":"CHRISTIAN","family":"MIRA","sequence":"first","affiliation":[{"name":"19 rue d'Occitanie, Fonsegrives, 31130 QUINT, and Department of Economics and Quantitative Methods, University of Urbino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANNA","family":"AGLIARI","sequence":"additional","affiliation":[{"name":"Catholic University of Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LAURA","family":"GARDINI","sequence":"additional","affiliation":[{"name":"Department of Economics and Quantitative Methods, University of Urbino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740300762X"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015039"},{"key":"rf4","first-page":"161","volume":"47","author":"Fatou P.","journal-title":"Bull. 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