{"id":"https://openalex.org/W1999790455","doi":"https://doi.org/10.1137/140978661","title":"Bifurcation of Relative Equilibria of the (1+3)-Body Problem","display_name":"Bifurcation of Relative Equilibria of the (1+3)-Body Problem","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1999790455","doi":"https://doi.org/10.1137/140978661","mag":"1999790455"},"language":"en","primary_location":{"id":"doi:10.1137/140978661","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140978661","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/2117/28007","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020795093","display_name":"Montserrat Corbera","orcid":"https://orcid.org/0000-0002-0367-9667"},"institutions":[{"id":"https://openalex.org/I115304662","display_name":"Universitat de Vic - Universitat Central de Catalunya","ror":"https://ror.org/006zjws59","country_code":"ES","type":"education","lineage":["https://openalex.org/I115304662"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Montserrat Corbera","raw_affiliation_strings":["The University of Vic - Central University of Catalonia"],"affiliations":[{"raw_affiliation_string":"The University of Vic - Central University of Catalonia","institution_ids":["https://openalex.org/I115304662"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065814685","display_name":"Josep M. Cors","orcid":"https://orcid.org/0000-0002-9803-8490"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Josep Cors","raw_affiliation_strings":["Polytechnic University of Catalonia"],"affiliations":[{"raw_affiliation_string":"Polytechnic University of Catalonia","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046015548","display_name":"Jaume Llibre","orcid":"https://orcid.org/0000-0002-9511-5999"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jaume Llibre","raw_affiliation_strings":["Autonomous University of Barcelona"],"affiliations":[{"raw_affiliation_string":"Autonomous University of Barcelona","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083807297","display_name":"Richard Moeckel","orcid":"https://orcid.org/0000-0001-8257-7126"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Moeckel","raw_affiliation_strings":["School of Mathematics, University of Minnesota, Minneapolis, MN 55455"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, MN 55455","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5020795093"],"corresponding_institution_ids":["https://openalex.org/I115304662"],"apc_list":null,"apc_paid":null,"fwci":19.2477,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.98699915,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"47","issue":"2","first_page":"1377","last_page":"1404"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10325","display_name":"Astro and Planetary Science","score":0.9769999980926514,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8358314037322998},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6865112781524658},{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.6781152486801147},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.6522773504257202},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5551309585571289},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5346680283546448},{"id":"https://openalex.org/keywords/n-body-problem","display_name":"n-body problem","score":0.4502635598182678},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.43731749057769775},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42693933844566345},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.417776882648468},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20400595664978027},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.17521655559539795},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14327499270439148},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08268776535987854}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8358314037322998},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6865112781524658},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.6781152486801147},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.6522773504257202},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5551309585571289},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5346680283546448},{"id":"https://openalex.org/C76941334","wikidata":"https://www.wikidata.org/wiki/Q1199050","display_name":"n-body problem","level":2,"score":0.4502635598182678},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.43731749057769775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42693933844566345},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.417776882648468},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20400595664978027},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.17521655559539795},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14327499270439148},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08268776535987854},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/140978661","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140978661","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:upcommons.upc.edu:2117/28007","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/28007","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:ddd.uab.cat:145289","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/145289","pdf_url":"https://ddd.uab.cat/record/145289","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:dnet:recercat____::977827015e5854fa86068295d0440bc2","is_oa":false,"landing_page_url":"http://hdl.handle.net/10854/4046","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dnet:uabarcelona_::f2cd5b728f380d12970da013ec109912","is_oa":false,"landing_page_url":"http://ddd.uab.cat/record/145289","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/28007","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/28007","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1558046443","display_name":null,"funder_award_id":"318999","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G2046735434","display_name":null,"funder_award_id":"316338 and 318999","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G3609606540","display_name":null,"funder_award_id":"MTM2013-40998-P","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G4695621433","display_name":null,"funder_award_id":"SGR 568","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G472310386","display_name":null,"funder_award_id":"2014SGR 568","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G5018646640","display_name":null,"funder_award_id":"DMS-1208908","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6546924280","display_name":null,"funder_award_id":"316338","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G7237708296","display_name":"Hamiltonian and Celestial Mechanics","funder_award_id":"1208908","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8117751741","display_name":null,"funder_award_id":"MTM2008-03437","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334830","display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","ror":"https://ror.org/01n4pqe45"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W588295442","https://openalex.org/W645859364","https://openalex.org/W653670463","https://openalex.org/W1488887332","https://openalex.org/W1625607527","https://openalex.org/W1674576174","https://openalex.org/W1965505736","https://openalex.org/W1970826019","https://openalex.org/W1972799934","https://openalex.org/W1975422833","https://openalex.org/W1981596975","https://openalex.org/W1993108081","https://openalex.org/W1996505038","https://openalex.org/W2008879265","https://openalex.org/W2026434926","https://openalex.org/W2040177652","https://openalex.org/W2043512351","https://openalex.org/W2050338848","https://openalex.org/W2051109533","https://openalex.org/W2053967969","https://openalex.org/W2058527002","https://openalex.org/W2073426911","https://openalex.org/W2077502044","https://openalex.org/W2080618918","https://openalex.org/W2086083605","https://openalex.org/W2088172592","https://openalex.org/W2090850711","https://openalex.org/W2096828612","https://openalex.org/W2098014885","https://openalex.org/W2122696655","https://openalex.org/W2129222951","https://openalex.org/W2156971036","https://openalex.org/W2163217780","https://openalex.org/W2331423321","https://openalex.org/W2473060496","https://openalex.org/W3105021676","https://openalex.org/W3105945846"],"related_works":["https://openalex.org/W2370598571","https://openalex.org/W2355499472","https://openalex.org/W2349230259","https://openalex.org/W2370818987","https://openalex.org/W41589661","https://openalex.org/W2350226651","https://openalex.org/W2361379965","https://openalex.org/W2385204246","https://openalex.org/W2385510272","https://openalex.org/W2348667803"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,6,10,21,27,30,33,52,61,75,82],"relative":[3,36,46,58,72,90],"equilibria":[4,37,47,73],"of":[5,9,29,35,44,60,71,74,81,98],"limit":[7],"case":[8],"planar":[11],"Newtonian":[12],"4-body":[13,77],"problem":[14,63,78],"when":[15,79],"three":[16,80],"masses":[17,32,83,94],"tend":[18],"to":[19,41,67,96],"zero,":[20],"so-called":[22],"(1+3)-body":[23,62],"problem.":[24],"Depending":[25],"on":[26],"values":[28],"infinitesimal":[31],"number":[34],"varies":[38],"from":[39],"ten":[40],"fourteen.":[42],"Six":[43],"these":[45,93,99],"are":[48,54,84],"always":[49],"convex,":[50],"and":[51,87],"others":[53],"concave.":[55],"Each":[56],"convex":[57,89],"equilibrium":[59,91],"can":[64],"be":[65],"continued":[66],"a":[68],"unique":[69],"family":[70],"general":[76],"sufficiently":[85],"small":[86],"every":[88],"for":[92],"belongs":[95],"one":[97],"six":[100],"families.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
