{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:20:35Z","timestamp":1772284835210,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,11]]},"abstract":"<jats:p> This work studies periodic orbits as action minimizers in the spatial isosceles three-body problem with mass [Formula: see text]. In each period, the body with mass [Formula: see text] moves up and down on a vertical line, while the other two bodies have the same mass [Formula: see text], and rotate about this vertical line symmetrically. For given [Formula: see text], such periodic orbits form a one-parameter set with a rotation angle [Formula: see text] as the parameter. <\/jats:p><jats:p> [Formula: see text]Two new phenomena are found for this set. First, for each [Formula: see text], this set of periodic orbits bifurcate from a circular Euler (central configuration) orbit to a Broucke (collision) orbit as [Formula: see text] increases from [Formula: see text] to [Formula: see text]. There exists a critical rotation angle [Formula: see text], where the orbit is a circular Euler orbit if [Formula: see text]; a spatial orbit if [Formula: see text]; and a Broucke (collision) orbit if [Formula: see text]. The exact formula of [Formula: see text] is numerically proved to be [Formula: see text]. Second, oscillating behaviors occur at rotation angle [Formula: see text] for all [Formula: see text]. Actually, the orbit with [Formula: see text] runs on its initial periodic shape for only a few periods. It breaks the first periodic shape and becomes irregular in a moment. However, it runs close to a different periodic shape after a while. In a short time, it falls apart from the second periodic shape and runs irregularly again. Such oscillation continues as time [Formula: see text] increases. Up to [Formula: see text], the orbit is bounded and keeps oscillating between periodic shapes and irregular motions. Further study implies that, for each [Formula: see text], the angle between any two consecutive periodic shapes is a constant. When [Formula: see text], similar oscillating behaviors are expected. <\/jats:p>","DOI":"10.1142\/s0218127415501692","type":"journal-article","created":{"date-parts":[[2015,12,3]],"date-time":"2015-12-03T06:30:18Z","timestamp":1449124218000},"page":"1550169","source":"Crossref","is-referenced-by-count":5,"title":["New Phenomena in the Spatial Isosceles Three-Body Problem with Unequal Masses"],"prefix":"10.1142","volume":"25","author":[{"given":"Duokui","family":"Yan","sequence":"first","affiliation":[{"name":"School of Mathematics and System Science, Beihang University, Beijing 100191, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rongchang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and System Science, Beihang University, Beijing 100191, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingwei","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematics and System Science, Beihang University, Beijing 100191, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weize","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Mathematics and System Science, Beihang University, Beijing 100191, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiancheng","family":"Ouyang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Brigham Young University, Provo 84602, Utah, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,12,2]]},"reference":[{"key":"S0218127415501692BIB1","first-page":"303","volume":"73","author":"Broucke R.","year":"1979","journal-title":"Astron. Astrophys."},{"key":"S0218127415501692BIB2","doi-asserted-by":"publisher","DOI":"10.1196\/annals.1311.023"},{"key":"S0218127415501692BIB3","first-page":"135","volume":"18","author":"Cabral H.","year":"2012","journal-title":"Bol. Soc. Mat. Mexicana"},{"key":"S0218127415501692BIB4","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-005-0413-2"},{"key":"S0218127415501692BIB5","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2008.167.325"},{"key":"S0218127415501692BIB6","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2012.v19.n2.a19"},{"key":"S0218127415501692BIB7","doi-asserted-by":"publisher","DOI":"10.2307\/2661357"},{"key":"S0218127415501692BIB9","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141002407880"},{"key":"S0218127415501692BIB10","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-003-0322-7"},{"key":"S0218127415501692BIB11","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09724-4_11"},{"key":"S0218127415501692BIB12","doi-asserted-by":"publisher","DOI":"10.1137\/0515065"},{"key":"S0218127415501692BIB13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.70.3675"},{"key":"S0218127415501692BIB14","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2009.2.379"},{"key":"S0218127415501692BIB15","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-2012-42-5-1601"},{"key":"S0218127415501692BIB16","first-page":"141","volume":"13","author":"Shibayama M.","year":"2009","journal-title":"RIMS K\u00f4ky\u00fbroku Bessatsu B"},{"key":"S0218127415501692BIB17","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-011-9338-2"},{"key":"S0218127415501692BIB18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8268-2_6"},{"key":"S0218127415501692BIB19","doi-asserted-by":"publisher","DOI":"10.1196\/annals.1311.024"},{"key":"S0218127415501692BIB20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.12.024"},{"key":"S0218127415501692BIB21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.10.032"},{"key":"S0218127415501692BIB22","first-page":"1550116-1","volume":"25","author":"Yan D","year":"2014","journal-title":"Int. J. Bifurcation and Chaos"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127415501692","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:05:48Z","timestamp":1565147148000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127415501692"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11]]},"references-count":21,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2015,12,2]]},"published-print":{"date-parts":[[2015,11]]}},"alternative-id":["10.1142\/S0218127415501692"],"URL":"https:\/\/doi.org\/10.1142\/s0218127415501692","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11]]}}}