{"id":"https://openalex.org/W3168031109","doi":"https://doi.org/10.1142/s0218127421500838","title":"Global Phase Portraits for the Kukles Systems of Degree 3 with \u21242-Reversible Symmetries","display_name":"Global Phase Portraits for the Kukles Systems of Degree 3 with \u21242-Reversible Symmetries","publication_year":2021,"publication_date":"2021-05-01","ids":{"openalex":"https://openalex.org/W3168031109","doi":"https://doi.org/10.1142/s0218127421500838","mag":"3168031109"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421500838","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421500838","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":"http://hdl.handle.net/11449/207805","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043763784","display_name":"Fabio Scalco Dias","orcid":"https://orcid.org/0000-0003-0635-4056"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Fabio Scalco Dias","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP 37.500\u2013903, Itajub\u00e1, MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, Avenida BPS 1303, Pinheirinho, CEP 37.500\u2013903, Itajub\u00e1, MG, Brazil","institution_ids":["https://openalex.org/I8165072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085486855","display_name":"Ronisio Moises Ribeiro","orcid":"https://orcid.org/0000-0001-8094-130X"},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ronisio Moises Ribeiro","raw_affiliation_strings":["Departamento de Matem\u00e1tica, IBILCE\u2013UNESP, Rua C. Colombo, 2265, CEP 15054-000, S. J. Rio Preto, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, IBILCE\u2013UNESP, Rua C. Colombo, 2265, CEP 15054-000, S. J. Rio Preto, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I879563668"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070562969","display_name":"Cl\u00e0ud\u00eca Valls","orcid":"https://orcid.org/0000-0001-8279-1229"},"institutions":[{"id":"https://openalex.org/I203847022","display_name":"Instituto Polit\u00e9cnico de Lisboa","ror":"https://ror.org/04ea70f07","country_code":"PT","type":"education","lineage":["https://openalex.org/I203847022"]},{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Claudia Valls","raw_affiliation_strings":["Departamento de Matem\u00e0tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e0tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal","institution_ids":["https://openalex.org/I203847022","https://openalex.org/I141596103"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5043763784"],"corresponding_institution_ids":["https://openalex.org/I8165072"],"apc_list":null,"apc_paid":null,"fwci":1.2463,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7826816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"06","first_page":"2150083","last_page":"2150083"},"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":0.9990000128746033,"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":0.9990000128746033,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9221000075340271,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/phase-portrait","display_name":"Phase portrait","score":0.9567922353744507},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.7984989285469055},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7911592721939087},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.681263267993927},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6340739130973816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5764232277870178},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5568446516990662},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5255923271179199},{"id":"https://openalex.org/keywords/phase-diagram","display_name":"Phase diagram","score":0.4574964642524719},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.3726028800010681},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3475494384765625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3445817232131958},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3319584131240845},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3290785551071167},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24157726764678955},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.179403156042099},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11418193578720093},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.057461947202682495}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.9567922353744507},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.7984989285469055},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7911592721939087},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.681263267993927},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6340739130973816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5764232277870178},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5568446516990662},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5255923271179199},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.4574964642524719},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3726028800010681},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3475494384765625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3445817232131958},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3319584131240845},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3290785551071167},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24157726764678955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.179403156042099},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11418193578720093},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.057461947202682495},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127421500838","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421500838","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:repositorio.unesp.br:11449/207805","is_oa":true,"landing_page_url":"http://hdl.handle.net/11449/207805","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UNESP","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorio.unesp.br:11449/207805","is_oa":true,"landing_page_url":"http://hdl.handle.net/11449/207805","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UNESP","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2890287661","display_name":null,"funder_award_id":"APQ-01158-17","funder_id":"https://openalex.org/F4320322980","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais"},{"id":"https://openalex.org/G3847369941","display_name":null,"funder_award_id":"UID/MAT/04459/2019","funder_id":"https://openalex.org/F4320335059","funder_display_name":"Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa"},{"id":"https://openalex.org/G4638325629","display_name":null,"funder_award_id":"2019/07316-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322980","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","ror":"https://ror.org/00nc55f03"},{"id":"https://openalex.org/F4320335059","display_name":"Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa","ror":"https://ror.org/02xankh89"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1515307033","https://openalex.org/W2013766837","https://openalex.org/W2027868522","https://openalex.org/W2061361830","https://openalex.org/W2163453170","https://openalex.org/W2584167599","https://openalex.org/W2607851375","https://openalex.org/W3091863431","https://openalex.org/W4250436454"],"related_works":["https://openalex.org/W2978842908","https://openalex.org/W2607851375","https://openalex.org/W2015939075","https://openalex.org/W2889027666","https://openalex.org/W3138933321","https://openalex.org/W2366108680","https://openalex.org/W2050778660","https://openalex.org/W2997369424","https://openalex.org/W3168031109","https://openalex.org/W2029939732"],"abstract_inverted_index":{"We":[0],"provide":[1],"the":[2,5,9,14],"normal":[3],"forms,":[4],"bifurcation":[6],"diagrams":[7],"and":[8],"global":[10],"phase":[11],"portraits":[12],"on":[13],"Poincar\u00e9":[15],"disk":[16],"of":[17,22],"all":[18],"planar":[19],"Kukles":[20],"systems":[21],"degree":[23],"[Formula:":[24,28],"see":[25,29],"text]":[26],"with":[27],"text]-symmetries.":[30]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}