{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T07:39:02Z","timestamp":1773387542648,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,8,20]],"date-time":"2022-08-20T00:00:00Z","timestamp":1660953600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,8,20]],"date-time":"2022-08-20T00:00:00Z","timestamp":1660953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Asociaci\u00f3n Mexicana de Cultura A.C."},{"name":"CONACYT M\u00e9xico","award":["A1S10112"],"award-info":[{"award-number":["A1S10112"]}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11801537"],"award-info":[{"award-number":["11801537"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201806345013"],"award-info":[{"award-number":["201806345013"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s00332-022-09824-7","type":"journal-article","created":{"date-parts":[[2022,8,20]],"date-time":"2022-08-20T19:35:41Z","timestamp":1661024141000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stability of Regular Polygonal Relative Equilibria on $$\\mathbf{}\\mathbb S^2$$"],"prefix":"10.1007","volume":"32","author":[{"given":"Antonio","family":"Hern\u00e1ndez-Gardu\u00f1o","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ernesto","family":"P\u00e9rez-Chavela","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6216-2326","authenticated-orcid":false,"given":"Shuqiang","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,8,20]]},"reference":[{"key":"9824_CR1","doi-asserted-by":"crossref","unstructured":"Arnold, V.I., Kozlov, V.V., Neishtadt, A.I.: Mathematical aspects of classical and celestial mechanics. [Dynamical systems. III], Translated from the Russian original by E. Khukhro, 3rd edition, Encyclopaedia of Mathematical Sciences, 3. Springer, Berlin (2006)","DOI":"10.1007\/978-3-540-48926-9"},{"issue":"3","key":"9824_CR2","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1070\/RD2004v009n03ABEH000280","volume":"9","author":"AV Borisov","year":"2004","unstructured":"Borisov, A.V., Mamaev, I.S., Kilin, A.A.: Two-body problem on a sphere. Reduction, stochasticity, periodic orbits. Regul. Chaotic Dyn. 9(3), 265\u2013279 (2004)","journal-title":"Regul. Chaotic Dyn."},{"issue":"6","key":"9824_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10569-018-9835-7","volume":"130","author":"AV Borisov","year":"2018","unstructured":"Borisov, A.V., Garc\u00eda-Naranjo, L.C., Mamaev, I.S., Montaldi, J.: Reduction and relative equilibria for the two-body problem on spaces of constant curvature. Celest. Mech. Dyn. Astron. 130(6), 1\u201336 (2018)","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"9824_CR4","volume-title":"Theory of Equations","author":"WS Burnside","year":"1899","unstructured":"Burnside, W.S., Panton, A.R.: Theory of Equations. Dublin University Press, Dublin (1899)"},{"key":"9824_CR5","unstructured":"Deng, Y., Zhu, S.: Odd index of the amended potential implies linear instability, arXiv:2106.06246v1"},{"issue":"5","key":"9824_CR6","doi-asserted-by":"publisher","first-page":"2783","DOI":"10.1090\/S0002-9947-2011-05558-3","volume":"364","author":"F Diacu","year":"2012","unstructured":"Diacu, F.: Polygonal homographic orbits of the curved N-body problem. Trans. Am. Math. Soc. 364(5), 2783\u20132802 (2012)","journal-title":"Trans. Am. Math. Soc."},{"key":"9824_CR7","first-page":"1071","volume":"228","author":"F Diacu","year":"2013","unstructured":"Diacu, F.: Relative equilibria of the 3-dimensional curved $$n$$-body problem. Mem. Am. Math. Soc. 228, 1071 (2013)","journal-title":"Mem. Am. Math. Soc."},{"issue":"1","key":"9824_CR8","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1016\/j.jde.2010.08.011","volume":"250","author":"F Diacu","year":"2011","unstructured":"Diacu, F., P\u00e9rez-Chavela, E.: Homographic solutions of the curved 3-body problem. J. Differ. Equ. 250(1), 340\u2013366 (2011)","journal-title":"J. Differ. Equ."},{"issue":"4","key":"9824_CR9","first-page":"1131","volume":"13","author":"F Diacu","year":"2020","unstructured":"Diacu, F., Zhu, S.: Almost all 3-body relative equilibria are inclined. Discrete Contin. Dyn. Syst. Ser. S 13(4), 1131\u20131143 (2020)","journal-title":"Discrete Contin. Dyn. Syst. Ser. S"},{"issue":"2","key":"9824_CR10","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s00332-011-9116-z","volume":"22","author":"F Diacu","year":"2012","unstructured":"Diacu, F., P\u00e9rez-Chavela, E., Santoprete, M.: The $$n$$-body problem in spaces of constant curvature: part I, relative equilibria. J. Nonlinear Sci. 22(2), 247\u2013266 (2012)","journal-title":"J. Nonlinear Sci."},{"issue":"257","key":"9824_CR11","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.physd.2013.04.007","volume":"256","author":"F Diacu","year":"2013","unstructured":"Diacu, F., Mart\u00ednez, R., P\u00e9rez-Chavela, E., Sim\u00f3, J.C.: On the stability of tetrahedral relative equilibria in the positively curved 4-body problem. Physica D 256(257), 21\u201335 (2013)","journal-title":"Physica D"},{"key":"9824_CR12","doi-asserted-by":"crossref","unstructured":"Diacu, F., S\u00e1nchez-Cerritos, J.M., Zhu, S.: Stability of fixed points and associated relative equilibria of the 3-body problem on $${\\mathbb{S}}^1$$ and $${\\mathbb{S}}^2$$. J. Dyn. Differ. Equ. 30(1), 209\u2013225 (2018a). Modification after publication at arXiv:1603.03339","DOI":"10.1007\/s10884-016-9550-6"},{"issue":"5","key":"9824_CR13","doi-asserted-by":"publisher","first-page":"1999","DOI":"10.1007\/s00332-018-9473-y","volume":"28","author":"F Diacu","year":"2018","unstructured":"Diacu, F., Stoica, C., Zhu, S.: Central configurations of the curved $$n$$-body problem. J. Nonlinear Sci. 28(5), 1999\u20132046 (2018b)","journal-title":"J. Nonlinear Sci."},{"issue":"7","key":"9824_CR14","doi-asserted-by":"publisher","first-page":"6375","DOI":"10.1016\/j.jde.2015.12.044","volume":"260","author":"LC Garc\u00eda-Naranjo","year":"2016","unstructured":"Garc\u00eda-Naranjo, L.C., Marrero, J.C., P\u00e9rez-Chavela, E., Rodr\u00edguez-Olmos, M.: Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2. J. Differ. Equ. 260(7), 6375\u20136404 (2016)","journal-title":"J. Differ. Equ."},{"key":"9824_CR15","unstructured":"Marsden, J.: Lectures on mechanics. In: London Mathematical Society Lecture Note Series, vol. 174. Cambridge University Press, Cambridge (1992)"},{"issue":"3","key":"9824_CR16","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.3934\/dcds.2013.33.1157","volume":"33","author":"R Mart\u00ednez","year":"2013","unstructured":"Mart\u00ednez, R., Sim\u00f3, J.C.: On the stability of the Lagrangian homographic solutions in a curved three-body problem on $${\\mathbb{S}}^2$$. Discrete Contin. Dyn. Syst. 33(3), 1157\u20131175 (2013)","journal-title":"Discrete Contin. Dyn. Syst."},{"issue":"2\u20133","key":"9824_CR17","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s10569-016-9750-8","volume":"128","author":"R Mart\u00ednez","year":"2017","unstructured":"Mart\u00ednez, R., Sim\u00f3, C.: Relative equilibria of the restricted three-body problem in curved spaces. Celest. Mech. Dyn. Astron. 128(2\u20133), 221\u2013259 (2017)","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"9824_CR18","doi-asserted-by":"crossref","unstructured":"Moeckel, R.: Linear stability analysis of some symmetrical classes of relative equilibria. In: Hamiltonian Dynamical Systems (Cincinnati, OH, 1992) (IMA Vol. Math. Appl. vol. 63), pp. 291\u2013317. Springer, New York","DOI":"10.1007\/978-1-4613-8448-9_20"},{"key":"9824_CR19","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/s00332-012-9142-5","volume":"22","author":"PK Newton","year":"2012","unstructured":"Newton, P.K., Ostrovskyi, V.: Energy-momentum stability of icosahedral configurations of point vortices on a sphere. J. Nonlinear Sci. 22, 499\u2013515 (2012)","journal-title":"J. Nonlinear Sci."},{"issue":"11","key":"9824_CR20","doi-asserted-by":"publisher","first-page":"5894","DOI":"10.1063\/1.532602","volume":"39","author":"S Pekarsky","year":"1998","unstructured":"Pekarsky, S., Marsden, J.E.: Point vortices on a sphere: stability of relative equilibria. J. Math. Phys. 39(11), 5894\u20135907 (1998)","journal-title":"J. Math. Phys."},{"issue":"2","key":"9824_CR21","doi-asserted-by":"publisher","first-page":"426","DOI":"10.4153\/CJM-2017-002-7","volume":"70","author":"E P\u00e9rez-Chavela","year":"2018","unstructured":"P\u00e9rez-Chavela, E., S\u00e1nchez-Cerritos, J.M.: Euler-type relative equilibria and their stability in spaces of constant curvature. Can. J. Math. 70(2), 426\u2013450 (2018)","journal-title":"Can. J. Math."},{"key":"9824_CR22","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1016\/j.cnsns.2018.07.022","volume":"67","author":"E P\u00e9rez-Chavela","year":"2019","unstructured":"P\u00e9rez-Chavela, E., S\u00e1nchez-Cerritos, J.M.: Hyperbolic relative equilibria for the negative curved $$n$$-body problem. Commun. Nonlinear Sci. Numer. Simul. 67, 460\u2013479 (2019)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"4","key":"9824_CR23","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1088\/0951-7715\/12\/4\/302","volume":"12","author":"GE Roberts","year":"1999","unstructured":"Roberts, G.E.: Spectral instability of relative equilibria in the planar n-body problem. Nonlinearity 12(4), 757\u2013769 (1999)","journal-title":"Nonlinearity"},{"issue":"46","key":"9824_CR24","doi-asserted-by":"publisher","first-page":"14405","DOI":"10.1088\/0305-4470\/39\/46\/012","volume":"39","author":"T Schmah","year":"2006","unstructured":"Schmah, T., Stoica, C.: Stability for Lagrangian relative equilibria of three-point-mass systems. J. Phys. A 39(46), 14405\u201314425 (2006)","journal-title":"J. Phys. A"},{"issue":"1","key":"9824_CR25","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF01881678","volume":"115","author":"JC Simo","year":"1991","unstructured":"Simo, J.C., Lewis, D., Marsden, J.E.: Stability of relative equilibria. I. The reduced energy-momentum method. Arch. Ration. Mech. Anal. 115(1), 15\u201359 (1991)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"10","key":"9824_CR26","doi-asserted-by":"publisher","first-page":"6191","DOI":"10.1016\/j.jde.2018.01.032","volume":"264","author":"C Stoica","year":"2018","unstructured":"Stoica, C.: On the $$n$$-body problem on surfaces of revolution. J. Differ. Equ. 264(10), 6191\u20136225 (2018)","journal-title":"J. Differ. Equ."},{"key":"9824_CR27","unstructured":"Wolfram Research, Inc. Mathematica, version 11.3 (2018)"},{"issue":"2","key":"9824_CR28","doi-asserted-by":"publisher","first-page":"1071","DOI":"10.1007\/s10884-020-09848-1","volume":"33","author":"X Yu","year":"2021","unstructured":"Yu, X., Zhu, S.: Regular polygonal equilibrium configurations on $${\\mathbb{S} }^1$$ and stability of the associated relative equilibria. J. Dyn. Differ. Equ. 33(2), 1071\u20131086 (2021)","journal-title":"J. Dyn. Differ. Equ."},{"issue":"3","key":"9824_CR29","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1134\/S1560354721030035","volume":"26","author":"S Zhu","year":"2021","unstructured":"Zhu, S.: Compactness and index of ordinary central configurations for the curved $$N$$-body problem. Regul. Chaotic Dyn. 26(3), 236\u2013257 (2021)","journal-title":"Regul. Chaotic Dyn."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-022-09824-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-022-09824-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-022-09824-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T15:46:43Z","timestamp":1661874403000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-022-09824-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,20]]},"references-count":29,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["9824"],"URL":"https:\/\/doi.org\/10.1007\/s00332-022-09824-7","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,20]]},"assertion":[{"value":"23 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 June 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 August 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"73"}}