{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T01:38:18Z","timestamp":1787017098992,"version":"3.56.0"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,2]]},"abstract":"<jats:p>\n                    In this paper, we consider the family of rational maps [Formula: see text] where n \u2265 2, d \u2265 1, and \u03bb \u2208 \u2102. We consider the case where \u03bb lies in the main cardioid of one of the n - 1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps F\n                    <jats:sub>\u03bb<\/jats:sub>\n                    and F\n                    <jats:sub>\u03bc<\/jats:sub>\n                    are conjugate on these Julia sets only if the parameters at the centers of the given cardioids satisfy \u03bc = \u03bd\n                    <jats:sup>j(d+1)<\/jats:sup>\n                    \u03bb or [Formula: see text] where j \u2208 \u2124 and \u03bd is an (n - 1)th root of unity. We define a dynamical invariant, which we call the minimal rotation number. It determines which of these maps are conjugate on their Julia sets, and we obtain an exact count of the number of distinct conjugacy classes of maps drawn from these main cardioids.\n                  <\/jats:p>","DOI":"10.1142\/s0218127413300048","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T05:55:17Z","timestamp":1363758917000},"page":"1330004","source":"Crossref","is-referenced-by-count":6,"title":["CHECKERBOARD JULIA SETS FOR RATIONAL MAPS"],"prefix":"10.1142","volume":"23","author":[{"given":"PAUL","family":"BLANCHARD","sequence":"first","affiliation":[{"name":"Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"F\u0130GEN","family":"\u00c7\u0130L\u0130NG\u0130R","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"DANIEL","family":"CUZZOCREO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ROBERT L.","family":"DEVANEY","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"DANIEL M.","family":"LOOK","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ELIZABETH D.","family":"RUSSELL","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2013,3,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385704000380"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11784-010-0003-2"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02972685"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2005.13.1035"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2005.54.2615"},{"key":"p_7","first-page":"163","volume":"30","author":"Devaney R. 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Math."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127413300048","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:04:45Z","timestamp":1565078685000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127413300048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2]]},"references-count":11,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2013,3,20]]},"published-print":{"date-parts":[[2013,2]]}},"alternative-id":["10.1142\/S0218127413300048"],"URL":"https:\/\/doi.org\/10.1142\/s0218127413300048","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2]]}}}