{"id":"https://openalex.org/W2022079858","doi":"https://doi.org/10.1142/s0218127414500904","title":"Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields","display_name":"Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields","publication_year":2014,"publication_date":"2014-07-01","ids":{"openalex":"https://openalex.org/W2022079858","doi":"https://doi.org/10.1142/s0218127414500904","mag":"2022079858"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414500904","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500904","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/A5086941202","display_name":"Tiago Carvalho","orcid":"https://orcid.org/0000-0003-3927-938X"},"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":"Tiago de Carvalho","raw_affiliation_strings":["Faculdade de Ci\u00eancias, Departamento de Matem\u00e1tica, Universidade Estadual Paulista, Rua Eng. Luiz Edmundo Carrijo Coube, 14-01 Bauru, S\u00e3o Paulo, Brasil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculdade de Ci\u00eancias, Departamento de Matem\u00e1tica, Universidade Estadual Paulista, Rua Eng. Luiz Edmundo Carrijo Coube, 14-01 Bauru, S\u00e3o Paulo, Brasil","institution_ids":["https://openalex.org/I879563668"]}]},{"author_position":"last","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, Campus Samambaia, Goi\u00e2nia, Goi\u00e1s, Brasil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, Campus Samambaia, Goi\u00e2nia, Goi\u00e1s, Brasil","institution_ids":["https://openalex.org/I68106152"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1682,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.8571832,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"07","first_page":"1450090","last_page":"1450090"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/codimension","display_name":"Codimension","score":0.945595920085907},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7981328368186951},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.785729169845581},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7062060832977295},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6022265553474426},{"id":"https://openalex.org/keywords/piecewise-linear-manifold","display_name":"Piecewise linear manifold","score":0.5723600387573242},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5535882711410522},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.48802557587623596},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.467816561460495},{"id":"https://openalex.org/keywords/complex-lamellar-vector-field","display_name":"Complex lamellar vector field","score":0.4664912223815918},{"id":"https://openalex.org/keywords/homeomorphism","display_name":"Homeomorphism (graph theory)","score":0.45914480090141296},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.44260168075561523},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.4164992570877075},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3904620110988617},{"id":"https://openalex.org/keywords/solenoidal-vector-field","display_name":"Solenoidal vector field","score":0.22423487901687622},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20485079288482666},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1721060574054718},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1612359881401062}],"concepts":[{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.945595920085907},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7981328368186951},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.785729169845581},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7062060832977295},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6022265553474426},{"id":"https://openalex.org/C184175843","wikidata":"https://www.wikidata.org/wiki/Q7191425","display_name":"Piecewise linear manifold","level":3,"score":0.5723600387573242},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5535882711410522},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.48802557587623596},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.467816561460495},{"id":"https://openalex.org/C112280298","wikidata":"https://www.wikidata.org/wiki/Q5156582","display_name":"Complex lamellar vector field","level":4,"score":0.4664912223815918},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.45914480090141296},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.44260168075561523},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.4164992570877075},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3904620110988617},{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.22423487901687622},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20485079288482666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1721060574054718},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1612359881401062},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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":2,"locations":[{"id":"doi:10.1142/s0218127414500904","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500904","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:11449/117213","is_oa":false,"landing_page_url":"http://hdl.handle.net/11449/117213","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W619317343","https://openalex.org/W1479782356","https://openalex.org/W1558079603","https://openalex.org/W1564263151","https://openalex.org/W1580276924","https://openalex.org/W1592648094","https://openalex.org/W1969176110","https://openalex.org/W1970812836","https://openalex.org/W1988912567","https://openalex.org/W1996518355","https://openalex.org/W2015821261","https://openalex.org/W2046609995","https://openalex.org/W2047449028","https://openalex.org/W2053511179","https://openalex.org/W2053758441","https://openalex.org/W2059380896","https://openalex.org/W2065618801","https://openalex.org/W2068413098","https://openalex.org/W2089466166","https://openalex.org/W2118742026","https://openalex.org/W2152871707","https://openalex.org/W2165411099","https://openalex.org/W2165871977","https://openalex.org/W2182274314","https://openalex.org/W2331926411","https://openalex.org/W3021145540","https://openalex.org/W4230378422","https://openalex.org/W4238307931"],"related_works":["https://openalex.org/W2949587959","https://openalex.org/W4298038193","https://openalex.org/W2127704724","https://openalex.org/W1997913704","https://openalex.org/W4299566625","https://openalex.org/W4297965753","https://openalex.org/W2737930328","https://openalex.org/W1558492989","https://openalex.org/W2886703350","https://openalex.org/W2022079858"],"abstract_inverted_index":{"In":[0,14],"this":[1,22],"paper,":[2],"we":[3],"are":[4],"dealing":[5],"with":[6],"piecewise":[7,38],"smooth":[8,39],"vector":[9,40],"fields":[10],"in":[11],"a":[12,16,35],"2D-manifold.":[13],"such":[15],"scenario,":[17],"the":[18,27,31,43],"main":[19],"goal":[20],"of":[21],"paper":[23],"is":[24],"to":[25],"exhibit":[26],"homeomorphism":[28],"that":[29],"gives":[30],"topological":[32],"equivalence":[33],"between":[34],"codimension":[36],"one":[37],"field":[41],"and":[42],"respective":[44],"C0-normal":[45],"form.":[46]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2025-10-10T00:00:00"}
