{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:12:34Z","timestamp":1786619554490,"version":"build-2736575974"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,9,15]]},"abstract":"<jats:p> In this paper, we investigate the stability of equilibrium points for the planar restricted equilateral four-body problem in the case that one particle of negligible mass is moving under the Newtonian gravitational attraction of three positive masses [Formula: see text], [Formula: see text] and [Formula: see text] (called primaries). These always lie at the vertices of an equilateral triangle (Lagrangian configuration) and move with constant angular velocity in circular orbits around their center of masses. We consider the case where all the primaries have unequal masses, and investigate the nonlinear stability (in the sense of Lyapunov) of the elliptic equilibrium for the specific values of the mass [Formula: see text] and [Formula: see text] of the primary, fixed on the horizontal axis. Moreover, the [Formula: see text][Formula: see text]:[Formula: see text][Formula: see text] four-order resonant cases are determined and the stability is investigated. In this study, Markeev\u2019s theorem and Arnold\u2019s theorem become key ingredients. <\/jats:p>","DOI":"10.1142\/s0218127421300317","type":"journal-article","created":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T06:11:56Z","timestamp":1630563116000},"page":"2130031","source":"Crossref","is-referenced-by-count":6,"title":["Nonlinear Stability of Equilibrium Points in the Planar Equilateral Restricted Mass-Unequal Four-Body Problem"],"prefix":"10.1142","volume":"31","author":[{"given":"Jos\u00e9 Alejandro","family":"Zepeda Ram\u00edrez","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, UAM\u2013Iztapalapa, 09340 Iztapalapa, Mexico City, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martha","family":"Alvarez-Ram\u00edrez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, UAM\u2013Iztapalapa, 09340 Iztapalapa, Mexico City, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio","family":"Garc\u00eda","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, UAM\u2013Iztapalapa, 09340 Iztapalapa, Mexico City, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2021,9,2]]},"reference":[{"key":"S0218127421300317BIB001","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/181360"},{"key":"S0218127421300317BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414500928"},{"key":"S0218127421300317BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-014-9594-z"},{"key":"S0218127421300317BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s10509-015-2333-4"},{"key":"S0218127421300317BIB005","first-page":"255","volume":"137","author":"Arnold V. 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