{"id":"https://openalex.org/W2692842713","doi":"https://doi.org/10.1142/s0218127417501413","title":"Classical Planar Algebraic Curves Realizable by Quadratic Polynomial Differential Systems","display_name":"Classical Planar Algebraic Curves Realizable by Quadratic Polynomial Differential Systems","publication_year":2017,"publication_date":"2017-08-01","ids":{"openalex":"https://openalex.org/W2692842713","doi":"https://doi.org/10.1142/s0218127417501413","mag":"2692842713"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417501413","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417501413","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ddd.uab.cat/record/182525","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014887804","display_name":"Isaac A. Garc\u00eda","orcid":"https://orcid.org/0000-0001-6982-9632"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Isaac A. Garc\u00eda","raw_affiliation_strings":["Departament de Matem\u00e0tica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Catalonia, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Catalonia, Spain","institution_ids":["https://openalex.org/I15766328"]}]},{"author_position":"last","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":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014887804"],"corresponding_institution_ids":["https://openalex.org/I15766328"],"apc_list":null,"apc_paid":null,"fwci":0.4228,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59479773,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"09","first_page":"1750141","last_page":"1750141"},"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":1.0,"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":1.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.7723355293273926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7555158138275146},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6816118955612183},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5849504470825195},{"id":"https://openalex.org/keywords/quadratic-differential","display_name":"Quadratic differential","score":0.5829480886459351},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5640103220939636},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5520232915878296},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5246800780296326},{"id":"https://openalex.org/keywords/algebraic-curve","display_name":"Algebraic curve","score":0.49061694741249084},{"id":"https://openalex.org/keywords/algebraic-differential-equation","display_name":"Algebraic differential equation","score":0.4894086420536041},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.4402349591255188},{"id":"https://openalex.org/keywords/invariant-theory","display_name":"Invariant theory","score":0.4366813898086548},{"id":"https://openalex.org/keywords/invariant-polynomial","display_name":"Invariant polynomial","score":0.433186799287796},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4129793047904968},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3605811595916748},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3594992160797119},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.2599371671676636},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2529902458190918},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.22175827622413635},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.181382417678833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1080954372882843},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07598653435707092},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0730491578578949},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06013798713684082}],"concepts":[{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.7723355293273926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7555158138275146},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6816118955612183},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5849504470825195},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.5829480886459351},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5640103220939636},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5520232915878296},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5246800780296326},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.49061694741249084},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.4894086420536041},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.4402349591255188},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.4366813898086548},{"id":"https://openalex.org/C134530390","wikidata":"https://www.wikidata.org/wiki/Q2920801","display_name":"Invariant polynomial","level":4,"score":0.433186799287796},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4129793047904968},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3605811595916748},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3594992160797119},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2599371671676636},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2529902458190918},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.22175827622413635},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.181382417678833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1080954372882843},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07598653435707092},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0730491578578949},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06013798713684082},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0218127417501413","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417501413","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:dnet:raudl_______::79cafe13d4fd8dccab1518b1d9697ad1","is_oa":false,"landing_page_url":"http://hdl.handle.net/10459.1/59932","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repositori.udl.cat:10459.1/59932","is_oa":false,"landing_page_url":"https://doi.org/10.1142/S0218127417501413","pdf_url":null,"source":{"id":"https://openalex.org/S4306400812","display_name":"Repositori ObertUDL (University of Lleida)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I15766328","host_organization_name":"Universitat de Lleida","host_organization_lineage":["https://openalex.org/I15766328"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ddd.uab.cat:182525","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/182525","pdf_url":"https://ddd.uab.cat/record/182525","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:uabarcelona_::dcfed485e52667ea5a59f268f6292955","is_oa":false,"landing_page_url":"http://ddd.uab.cat/record/182525","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:ddd.uab.cat:182525","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/182525","pdf_url":"https://ddd.uab.cat/record/182525","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"},"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/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/G8246274189","display_name":null,"funder_award_id":"MTM2016-77278-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/G8956130658","display_name":null,"funder_award_id":"2014SGR 1204","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/F4320334830","display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","ror":"https://ror.org/01n4pqe45"},{"id":"https://openalex.org/F4320338368","display_name":"FP7 People: Marie-Curie Actions","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2692842713.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W594548925","https://openalex.org/W1498112751","https://openalex.org/W1972241390","https://openalex.org/W1972244924","https://openalex.org/W1981798823","https://openalex.org/W1997290261","https://openalex.org/W2004209019","https://openalex.org/W2014749888","https://openalex.org/W2044413922","https://openalex.org/W2049815318","https://openalex.org/W2080740553","https://openalex.org/W2105763874","https://openalex.org/W2162465934","https://openalex.org/W2332191372","https://openalex.org/W4240562712"],"related_works":["https://openalex.org/W1981823816","https://openalex.org/W4299166897","https://openalex.org/W2041754077","https://openalex.org/W586764485","https://openalex.org/W2167673968","https://openalex.org/W2508955291","https://openalex.org/W4297752434","https://openalex.org/W2154723430","https://openalex.org/W2753325906","https://openalex.org/W1023909028"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,20],"show":[4],"planar":[5,15],"quadratic":[6],"polynomial":[7],"differential":[8,30],"systems":[9],"exhibiting":[10],"as":[11],"solutions":[12],"some":[13],"famous":[14],"invariant":[16],"algebraic":[17],"curves.":[18],"Also":[19],"place":[21],"particular":[22],"attention":[23],"to":[24],"the":[25],"Darboux":[26],"integrability":[27],"of":[28],"these":[29],"systems.":[31]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}