{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:25:37Z","timestamp":1787318737196,"version":"build-2736575974"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2021,8,15]],"date-time":"2021-08-15T00:00:00Z","timestamp":1628985600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,15]],"date-time":"2021-08-15T00:00:00Z","timestamp":1628985600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s00332-021-09741-1","type":"journal-article","created":{"date-parts":[[2021,8,15]],"date-time":"2021-08-15T01:02:39Z","timestamp":1628989359000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stacked Central Configurations in the 5-Vortex Problem"],"prefix":"10.1007","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9297-5101","authenticated-orcid":false,"given":"A. C.","family":"Fernandes","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claudio","family":"Vidal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,8,15]]},"reference":[{"key":"9741_CR1","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1063\/1.2425103","volume":"48","author":"H Aref","year":"2007","unstructured":"Aref, H.: Point vortex dynamics: a classical mathematics playground. J. Math. Phys. 48, 35\u201358 (2007)","journal-title":"J. Math. Phys."},{"key":"9741_CR2","doi-asserted-by":"crossref","first-page":"321","DOI":"10.3406\/bastr.1918.13419","volume":"35","author":"J Chazy","year":"1918","unstructured":"Chazy, J.: Sur certaines trajectoires du probl\u00e8me des $$n$$ corps. Bull. Astron. 35, 321\u2013389 (1918)","journal-title":"Bull. Astron."},{"issue":"9","key":"9741_CR3","doi-asserted-by":"publisher","first-page":"1241","DOI":"10.1016\/j.geomphys.2008.05.003","volume":"58","author":"M Corbera","year":"2008","unstructured":"Corbera, M., Llibre, J.: Central configurations of nested regular polyhedra for the spatial $$2n$$-body problem. J. Geom. Phys. 58(9), 1241\u20131252 (2008)","journal-title":"J. Geom. Phys."},{"key":"9741_CR4","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s10569-017-9782-8","volume":"129","author":"JL Cornelio","year":"2017","unstructured":"Cornelio, J.L., \u00c1lvarez-Ram\u00edrez, M., Cors, J.M.: A family of stacked central configurations in the Planar five-body problem. Celest. Mech. Dyn. Astron. 129, 321\u2013328 (2017)","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"9741_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-018-9647-1","author":"JL Cornelio","year":"2018","unstructured":"Cornelio, J.L., \u00c1lvarez-Ram\u00edrez, M., Cors, J.M.: A special family of stacked central configurations: Lagrange plus Euler in one. J. Dyn. Differ. Equ. (2018). https:\/\/doi.org\/10.1007\/s10884-018-9647-1","journal-title":"J. Dyn. Differ. Equ."},{"key":"9741_CR6","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10569-009-9243-0","volume":"106","author":"M Gidea","year":"2010","unstructured":"Gidea, M., Llibre, J.: Symmetric planar central configurations of five bodies: Euler plus two. Celest. Mech. Dyn. Astron. 106, 89\u2013107 (2010)","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"9741_CR7","unstructured":"Gr\u00f6bli, W.: Specielle Probleme \u00fcber die Bewegung geradliniger paralleler Wirbelf\u00e4den. Z\u00fcrcher und Furrer, Z\u00fcrich. Republished in Vierteljahrschrift der naturforschenden Gesellschaft in Z\u00fcurich 22(37\u201381), 129\u2013167 (1877)"},{"key":"9741_CR8","volume-title":"Celestial Mechanics","author":"Y Hagihara","year":"1970","unstructured":"Hagihara, Y.: Celestial Mechanics, vol. 1. MIT Press, Massachusetts (1970)"},{"key":"9741_CR9","doi-asserted-by":"publisher","first-page":"2299","DOI":"10.1088\/0951-7715\/18\/5\/021","volume":"18","author":"M Hampton","year":"2005","unstructured":"Hampton, M.: Stacked central configurations: new examples in the planar five-body problem. Nonlinearity 18, 2299\u20132304 (2005)","journal-title":"Nonlinearity"},{"issue":"1","key":"9741_CR10","doi-asserted-by":"publisher","first-page":"35","DOI":"10.3934\/jgm.2015.7.35","volume":"7","author":"M Hampton","year":"2015","unstructured":"Hampton, M., Jensen, A.: Finiteness of relative equilibria in the planar generalized N-body problem with fixed subconfigurations. J. Geom. Mech. 7(1), 35\u201342 (2015)","journal-title":"J. Geom. Mech."},{"key":"9741_CR11","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s00222-005-0461-0","volume":"163","author":"M Hampton","year":"2006","unstructured":"Hampton, M., Moeckel, R.: Finiteness of relative equilibria of the four-body problem. Invent. Math. 163, 289\u2013312 (2006)","journal-title":"Invent. Math."},{"key":"9741_CR12","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s10569-007-9102-9","volume":"99","author":"M Hampton","year":"2007","unstructured":"Hampton, M., Santopetre, M.: Seven-body central configurations: a family of central configurations in the spatial seven-body problem. Celest. Mech. Dyn. Astron. 99, 293\u2013305 (2007)","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"9741_CR13","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s00332-013-9184-3","volume":"24","author":"M Hampton","year":"2014","unstructured":"Hampton, M., Roberts, G., Santoprete, M.: Relative equilibria in the four-vortex problem with two pairs of equal vorticities. J. Nonlinear Sci. 24, 39\u201392 (2014)","journal-title":"J. Nonlinear Sci."},{"key":"9741_CR14","volume-title":"Vorlesungen \u00fcber mathematische physik","author":"G Kirchhoff","year":"1883","unstructured":"Kirchhoff, G.: Vorlesungen \u00fcber mathematische physik. B.G. Teubner, Leipzig (1883)"},{"key":"9741_CR15","doi-asserted-by":"publisher","first-page":"2196","DOI":"10.1175\/1520-0469(2001)058<2196:MPFPAR>2.0.CO;2","volume":"58","author":"JP Kossin","year":"2001","unstructured":"Kossin, J.P., Schubet, W.H.: Mesovortices, polygonal flow patterns, and rapid pressure falls in hurricane-line vortices. J. Atmos. Sci. 58, 2196\u20132209 (2001)","journal-title":"J. Atmos. Sci."},{"issue":"2","key":"9741_CR16","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/s10569-007-9107-4","volume":"100","author":"J Llibre","year":"2008","unstructured":"Llibre, J., Mello, L.: New central configurations for the planar 5-body problem. Celest. Mech. Dyn. Astronom. 100(2), 141\u2013149 (2008)","journal-title":"Celest. Mech. Dyn. Astronom."},{"key":"9741_CR17","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/s10569-011-9342-6","volume":"110","author":"J Llibre","year":"2011","unstructured":"Llibre, J., Mello, L., P\u00e9rez, E.: New stacked central configurations for the planar 5-body problem. Celest. Mech. Dyn. Astronom. 110, 43\u201352 (2011)","journal-title":"Celest. Mech. Dyn. Astronom."},{"issue":"3","key":"9741_CR18","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1590\/S0102-47442007000300010","volume":"29","author":"L Mello","year":"2007","unstructured":"Mello, L., Fernandes, A.: Configura\u00e7oes centrais planares encaixantes. Rev. Bras. Ensino de F\u00edsica 29(3), 385\u2013388 (2007)","journal-title":"Rev. Bras. Ensino de F\u00edsica"},{"key":"9741_CR19","doi-asserted-by":"crossref","unstructured":"Mello, L.F., Fernandes, A.C.: On stacked central configurations with $$n$$ bodies when one body is removed. J. Math. Anal. Appl. 405, 320\u2013325 (2013a)","DOI":"10.1016\/j.jmaa.2013.04.016"},{"key":"9741_CR20","doi-asserted-by":"crossref","unstructured":"Mello, L.F., Fernandes, A.C.: On stacked central configurations with five bodies when one body is removed. Qual. Theory Dyn. Syst. 12, 292\u2013303 (2013b)","DOI":"10.1007\/s12346-012-0084-y"},{"key":"9741_CR21","doi-asserted-by":"crossref","unstructured":"Mello, L., Fernandes, A.: Stacked central configurations for the spatial seven-body problem. Qual. Theory Dyn. Syst. 12, 101\u2013114 (2013c)","DOI":"10.1007\/s12346-012-0073-1"},{"key":"9741_CR22","doi-asserted-by":"publisher","first-page":"1216","DOI":"10.1016\/j.geomphys.2009.06.004","volume":"59","author":"L Mello","year":"2009","unstructured":"Mello, L., Fernandes, A., Chaves, F., Garcia, B.: Stacked central configurations for the spatial six-body problem. J. Geom. Phys. 59, 1216\u20131226 (2009)","journal-title":"J. Geom. Phys."},{"key":"9741_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9290-3","volume-title":"The $$n$$-Vortex Problem: Analytical Techniques","author":"PK Newton","year":"2001","unstructured":"Newton, P.K.: The $$n$$-Vortex Problem: Analytical Techniques. Springer, Berlin (2001)"},{"key":"9741_CR24","doi-asserted-by":"publisher","first-page":"3715","DOI":"10.3934\/dcds.2012.32.3715","volume":"32","author":"A Oliveira","year":"2012","unstructured":"Oliveira, A., Cabral, H.: On stacked central configurations of the planar coorbital satellites problem. Discrete Contin. Dyn. Syst. 32, 3715\u20133732 (2012)","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"9741_CR25","doi-asserted-by":"crossref","unstructured":"O\u2019Neil, K.A.: Stationary configurations of point vortices. Trans. Am. Math. Soc. 302(2), 383\u2013425 (1987)","DOI":"10.2307\/2000850"},{"key":"9741_CR26","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1073\/pnas.79.2.716","volume":"79","author":"JI Palmore","year":"1982","unstructured":"Palmore, J.I.: Relative equilibria of vortices in two dimension. Proc. Natl. Acad. Sci. 79, 716\u2013718 (1982)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"3","key":"9741_CR27","first-page":"189","volume":"22","author":"E P\u00e9rez-Chavela","year":"2015","unstructured":"P\u00e9rez-Chavela, E., Santoprete, M., Tamayo, C.: Symmetric relative equilibria in the four-vortex problem with three equal vorticities. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 22(3), 189\u2013209 (2015)","journal-title":"Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal."},{"issue":"2","key":"9741_CR28","doi-asserted-by":"publisher","first-page":"1743","DOI":"10.1016\/j.jmaa.2016.09.055","volume":"446","author":"A Santos","year":"2017","unstructured":"Santos, A., Marchesin, M., P\u00e9rez-Chavela, E., Vidal, C.: Continuation and bifurcations of concave central configurations in the four and five body-problems for homogeneous force laws. J. Math. Anal. Appl. 446(2), 1743\u20131768 (2017)","journal-title":"J. Math. Anal. Appl."},{"key":"9741_CR29","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/S0034-4877(14)60012-4","volume":"72","author":"X Su","year":"2013","unstructured":"Su, X.: New stacked central configurations for the spatial seven-body problem. Rep. Math. Phys. 72, 179\u2013189 (2013)","journal-title":"Rep. Math. Phys."},{"key":"9741_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.geomphys.2013.10.007","volume":"76","author":"X Su","year":"2014","unstructured":"Su, X., Deng, C.: Two classes of stacked central configurations for the spatial $$2n + 1$$-body problem: nested regular polyhedra plus one. J. Geom. Phys. 76, 1\u20139 (2014)","journal-title":"J. Geom. Phys."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-021-09741-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-021-09741-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-021-09741-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,7]],"date-time":"2023-01-07T06:34:01Z","timestamp":1673073241000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-021-09741-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,15]]},"references-count":30,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["9741"],"URL":"https:\/\/doi.org\/10.1007\/s00332-021-09741-1","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,15]]},"assertion":[{"value":"23 December 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 August 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 August 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"83"}}