{"id":"https://openalex.org/W2050556108","doi":"https://doi.org/10.1142/s0218127410027593","title":"GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES","display_name":"GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES","publication_year":2010,"publication_date":"2010-10-01","ids":{"openalex":"https://openalex.org/W2050556108","doi":"https://doi.org/10.1142/s0218127410027593","mag":"2050556108"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127410027593","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410027593","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":true,"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"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059877036","display_name":"Marcelo Messias","orcid":"https://orcid.org/0000-0003-2269-7091"},"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":"MARCELO MESSIAS","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Estat\u00edstica e Computa\u00e7\u00e3o, Faculdade de Ci\u00eancias e Tecnologia, UNESP \u2013 Univ Estadual Paulista, Cx. Postal 266, 19060-900, Presidente Prudente, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Estat\u00edstica e Computa\u00e7\u00e3o, Faculdade de Ci\u00eancias e Tecnologia, UNESP \u2013 Univ Estadual Paulista, Cx. Postal 266, 19060-900, Presidente Prudente, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I879563668"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001277261","display_name":"Paulo Ricardo da Silva","orcid":"https://orcid.org/0000-0002-1430-5986"},"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":"PAULO RICARDO DA SILVA","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Instituto de Bioci\u00eancias, Letras e Ci\u00eancias Exatas, UNESP \u2013 Univ Estadual Paulista, Rua C. Colombo, 2265, 15054\u2013000, S. J. Rio Preto, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Instituto de Bioci\u00eancias, Letras e Ci\u00eancias Exatas, UNESP \u2013 Univ Estadual Paulista, Rua C. Colombo, 2265, 15054\u2013000, S. J. Rio Preto, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I879563668"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5046015548"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":null,"apc_paid":null,"fwci":3.36131132,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.90948158,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"10","first_page":"3137","last_page":"3155"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.7767913341522217},{"id":"https://openalex.org/keywords/compactification","display_name":"Compactification (mathematics)","score":0.7353013753890991},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7015489339828491},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6253449320793152},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6113643050193787},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.5566139817237854},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.442516028881073},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4044249653816223},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20081377029418945},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.1736297607421875},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.08417776226997375},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06709539890289307},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0670105516910553}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.7767913341522217},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.7353013753890991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7015489339828491},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6253449320793152},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6113643050193787},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.5566139817237854},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.442516028881073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4044249653816223},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20081377029418945},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1736297607421875},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.08417776226997375},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06709539890289307},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0670105516910553},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127410027593","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410027593","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:acervodigital.unesp.br:11449/7118","is_oa":false,"landing_page_url":"http://acervodigital.unesp.br/handle/11449/7118","pdf_url":null,"source":{"id":"https://openalex.org/S4306400256","display_name":"Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210115194","host_organization_name":"Funda\u00e7\u00e3o para o Desenvolvimento da UNESP","host_organization_lineage":["https://openalex.org/I4210115194"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"outro"},{"id":"pmh:oai:repositorio.unesp.br:11449/7118","is_oa":false,"landing_page_url":"http://hdl.handle.net/11449/7118","pdf_url":null,"source":{"id":"https://openalex.org/S4377196277","display_name":"UNESP Institutional Repository (S\u00e3o Paulo State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I879563668","host_organization_name":"Universidade Estadual Paulista (Unesp)","host_organization_lineage":["https://openalex.org/I879563668"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1965257932","https://openalex.org/W1971650444","https://openalex.org/W1983674368","https://openalex.org/W1995287688","https://openalex.org/W2016595627","https://openalex.org/W2029750936","https://openalex.org/W2048509006","https://openalex.org/W2058099048","https://openalex.org/W2071248198","https://openalex.org/W2071290058","https://openalex.org/W2100103560","https://openalex.org/W2141394518","https://openalex.org/W4231102510"],"related_works":["https://openalex.org/W2339458745","https://openalex.org/W3021650107","https://openalex.org/W1969643210","https://openalex.org/W2362177665","https://openalex.org/W2392476553","https://openalex.org/W2388265512","https://openalex.org/W4368370350","https://openalex.org/W2388954868","https://openalex.org/W3207663217","https://openalex.org/W2893349029"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"by":[3],"using":[4],"the":[5,13,17,37,48,54,57,70,75,78,83,89,94],"Poincar\u00e9":[6,79],"compactification":[7,84],"of":[8,16,53,74,85,93],"\u211d":[9,34,45,86],"3":[10,35,46,87],"we":[11,68],"describe":[12],"global":[14,71],"dynamics":[15],"Lorenz":[18,58],"system":[19,59,76],"[Formula:":[20],"see":[21],"text]":[22],"having":[23],"some":[24],"invariant":[25,61],"algebraic":[26,62],"surfaces.":[27,63],"Of":[28],"course":[29],"(x,":[30],"y,":[31],"z)":[32],"\u2208":[33,44],"are":[36,47],"state":[38],"variables":[39],"and":[40],"(s,":[41],"r,":[42],"b)":[43],"parameters.":[49],"For":[50,64],"six":[51,66],"sets":[52],"parameter":[55],"values,":[56],"has":[60],"these":[65],"sets,":[67],"provide":[69],"phase":[72],"portrait":[73],"in":[77,82],"ball":[80],"(i.e.":[81],"with":[88],"sphere":[90],"\ud835\udd4a":[91],"2":[92],"infinity).":[95]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
