{"id":"https://openalex.org/W2008879265","doi":"https://doi.org/10.1137/130911342","title":"Bifurcations and Enumeration of Classes of Relative Equilibria in the Planar Restricted Four-Body Problem","display_name":"Bifurcations and Enumeration of Classes of Relative Equilibria in the Planar Restricted Four-Body Problem","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2008879265","doi":"https://doi.org/10.1137/130911342","mag":"2008879265"},"language":"en","primary_location":{"id":"doi:10.1137/130911342","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911342","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067877484","display_name":"Jean Fernandes Barros","orcid":"https://orcid.org/0000-0001-9485-6149"},"institutions":[{"id":"https://openalex.org/I21606457","display_name":"Universidade Estadual de Feira de Santana","ror":"https://ror.org/04ygk5j35","country_code":"BR","type":"education","lineage":["https://openalex.org/I21606457"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jean F. Barros","raw_affiliation_strings":["State University of Feira De Santana"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State University of Feira De Santana","institution_ids":["https://openalex.org/I21606457"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019366771","display_name":"Eduardo S. G. Leandro","orcid":"https://orcid.org/0000-0002-7833-3492"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eduardo S. G. Leandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9693,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.90043197,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"46","issue":"2","first_page":"1185","last_page":"1203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9991999864578247,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9807999730110168,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9790999889373779,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8085595369338989},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.7826306819915771},{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.7383543252944946},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.6270347833633423},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5801801681518555},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5552908778190613},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5483537316322327},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5009982585906982},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4759271442890167},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46675944328308105},{"id":"https://openalex.org/keywords/three-body-problem","display_name":"Three-body problem","score":0.44002532958984375},{"id":"https://openalex.org/keywords/center-of-mass","display_name":"Center of mass (relativistic)","score":0.4342799484729767},{"id":"https://openalex.org/keywords/newtonian-fluid","display_name":"Newtonian fluid","score":0.42477312684059143},{"id":"https://openalex.org/keywords/n-body-problem","display_name":"n-body problem","score":0.42017483711242676},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32619935274124146},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2805339992046356},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.25715941190719604},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18536901473999023},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12217563390731812}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8085595369338989},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.7826306819915771},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.7383543252944946},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.6270347833633423},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5801801681518555},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5552908778190613},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5483537316322327},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5009982585906982},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4759271442890167},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46675944328308105},{"id":"https://openalex.org/C34725247","wikidata":"https://www.wikidata.org/wiki/Q607699","display_name":"Three-body problem","level":2,"score":0.44002532958984375},{"id":"https://openalex.org/C36185635","wikidata":"https://www.wikidata.org/wiki/Q17006925","display_name":"Center of mass (relativistic)","level":3,"score":0.4342799484729767},{"id":"https://openalex.org/C294558","wikidata":"https://www.wikidata.org/wiki/Q366968","display_name":"Newtonian fluid","level":2,"score":0.42477312684059143},{"id":"https://openalex.org/C76941334","wikidata":"https://www.wikidata.org/wiki/Q1199050","display_name":"n-body problem","level":2,"score":0.42017483711242676},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32619935274124146},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2805339992046356},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.25715941190719604},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18536901473999023},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12217563390731812},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C47513753","wikidata":"https://www.wikidata.org/wiki/Q3502299","display_name":"Energy\u2013momentum relation","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130911342","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911342","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W645859364","https://openalex.org/W1560124954","https://openalex.org/W1828839365","https://openalex.org/W1965505736","https://openalex.org/W1974384975","https://openalex.org/W2019708361","https://openalex.org/W2043512351","https://openalex.org/W2044413922","https://openalex.org/W2086083605","https://openalex.org/W2090850711","https://openalex.org/W2096828612","https://openalex.org/W2120250175","https://openalex.org/W2156971036","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2585886468","https://openalex.org/W3166098286","https://openalex.org/W3215164054","https://openalex.org/W2786896208","https://openalex.org/W2223963887","https://openalex.org/W2056102455","https://openalex.org/W2477085608","https://openalex.org/W2058001239","https://openalex.org/W2028734034","https://openalex.org/W833214278"],"abstract_inverted_index":{"The":[0],"planar":[1,9,64],"restricted":[2,65],"four-body":[3,66],"problem":[4,11,67],"consists":[5],"of":[6,16,49,62,105,107],"the":[7,23,41,58,63,82,86,102],"Newtonian":[8],"three-body":[10],"with":[12],"an":[13],"additional":[14],"body":[15],"infinitesimal":[17],"mass":[18,87],"which":[19,40],"is":[20,89],"attracted":[21],"by":[22,79],"three":[24],"bodies":[25,43],"(primaries)":[26],"but":[27],"has":[28],"no":[29],"gravitational":[30],"effect":[31],"on":[32],"them.":[33],"Relative":[34],"equilibria":[35,61],"are":[36],"special":[37],"solutions":[38],"in":[39,85],"four":[42],"rotate":[44],"uniformly":[45],"about":[46],"their":[47],"center":[48],"mass.":[50],"In":[51],"a":[52,69,90],"previous":[53],"article,":[54],"we":[55,75,96],"proved":[56],"that":[57,77,81],"degenerate":[59],"relative":[60,108],"form":[68],"simple,":[70,91],"closed,":[71,92],"analytic":[72],"curve.":[73],"Presently,":[74],"complement":[76],"work":[78],"showing":[80],"bifurcation":[83],"set":[84],"space":[88],"continuous":[93],"curve,":[94],"and":[95],"use":[97],"this":[98],"knowledge":[99],"to":[100],"provide":[101],"possible":[103],"numbers":[104],"classes":[106],"equilibria.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}