{"id":"https://openalex.org/W3089253439","doi":"https://doi.org/10.1142/s0218127420501631","title":"Crossing Periodic Orbits via First Integrals","display_name":"Crossing Periodic Orbits via First Integrals","publication_year":2020,"publication_date":"2020-09-15","ids":{"openalex":"https://openalex.org/W3089253439","doi":"https://doi.org/10.1142/s0218127420501631","mag":"3089253439"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420501631","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501631","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/236647","any_repository_has_fulltext":true},"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/A5043408154","display_name":"Durval J. Tonon","orcid":"https://orcid.org/0000-0002-2733-1825"},"institutions":[{"id":"https://openalex.org/I68106152","display_name":"Universidade Federal de Goi\u00e1s","ror":"https://ror.org/0039d5757","country_code":"BR","type":"education","lineage":["https://openalex.org/I68106152"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Durval Jos\u00e9 Tonon","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, CEP 74001-970, Caixa Postal 131 Goi\u00e2nia, Goi\u00e1s, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, CEP 74001-970, Caixa Postal 131 Goi\u00e2nia, Goi\u00e1s, Brazil","institution_ids":["https://openalex.org/I68106152"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023478976","display_name":"Mariana Queiroz Velter","orcid":"https://orcid.org/0000-0001-8713-2898"},"institutions":[{"id":"https://openalex.org/I68106152","display_name":"Universidade Federal de Goi\u00e1s","ror":"https://ror.org/0039d5757","country_code":"BR","type":"education","lineage":["https://openalex.org/I68106152"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Mariana Queiroz Velter","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, CEP 74001-970, Caixa Postal 131 Goi\u00e2nia, Goi\u00e1s, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, CEP 74001-970, Caixa Postal 131 Goi\u00e2nia, Goi\u00e1s, Brazil","institution_ids":["https://openalex.org/I68106152"]}]}],"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":1.1604,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77570287,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","issue":"11","first_page":"2050163","last_page":"2050163"},"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9782999753952026,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9388999938964844,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/periodic-orbits","display_name":"Periodic orbits","score":0.7514898180961609},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.6941981911659241},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6876248717308044},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6662868857383728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6315625905990601},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5046497583389282},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.497374564409256},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4512861371040344},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.42984020709991455},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20441526174545288},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1343960165977478},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.055720776319503784}],"concepts":[{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.7514898180961609},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.6941981911659241},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6876248717308044},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6662868857383728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6315625905990601},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5046497583389282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.497374564409256},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4512861371040344},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.42984020709991455},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20441526174545288},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1343960165977478},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.055720776319503784},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127420501631","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501631","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:ddd.uab.cat:236647","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/236647","pdf_url":null,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:recercat.cat:2072/445703","is_oa":false,"landing_page_url":"http://hdl.handle.net/2072/445703","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"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":{"id":"pmh:oai:ddd.uab.cat:236647","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/236647","pdf_url":null,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.41999998688697815,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W58398526","https://openalex.org/W416781817","https://openalex.org/W2015010497","https://openalex.org/W2019076112","https://openalex.org/W2731769483","https://openalex.org/W4230378422","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W1596838019","https://openalex.org/W3182827720","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W44694169","https://openalex.org/W2100864966","https://openalex.org/W2109304297","https://openalex.org/W2048650277","https://openalex.org/W2083709218"],"abstract_inverted_index":{"We":[0],"characterize":[1],"the":[2,39],"families":[3],"of":[4,7,26],"periodic":[5],"orbits":[6],"two":[8],"discontinuous":[9,28],"piecewise":[10,29],"differential":[11,30,36,43],"systems":[12,31],"in":[13],"[Formula:":[14],"see":[15],"text]":[16],"separated":[17],"by":[18,34,41],"a":[19],"plane":[20],"using":[21],"their":[22],"first":[23],"integrals.":[24],"One":[25],"these":[27],"is":[32],"formed":[33],"linear":[35],"systems,":[37],"and":[38],"other":[40],"nonlinear":[42],"systems.":[44]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
