{"id":"https://openalex.org/W2805247396","doi":"https://doi.org/10.1142/s0218127418500657","title":"Bifurcation Diagram of a Map with Multiple Critical Points","display_name":"Bifurcation Diagram of a Map with Multiple Critical Points","publication_year":2018,"publication_date":"2018-05-01","ids":{"openalex":"https://openalex.org/W2805247396","doi":"https://doi.org/10.1142/s0218127418500657","mag":"2805247396"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127418500657","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418500657","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/A5043273508","display_name":"M. Romera","orcid":"https://orcid.org/0000-0002-4814-3743"},"institutions":[{"id":"https://openalex.org/I134820265","display_name":"Consejo Superior de Investigaciones Cient\u00edficas","ror":"https://ror.org/02gfc7t72","country_code":"ES","type":"government","lineage":["https://openalex.org/I134820265"]},{"id":"https://openalex.org/I4210087408","display_name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n \u201cLeonardo Torres Quevedo\u201d","ror":"https://ror.org/00zsy6110","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. Romera","raw_affiliation_strings":["Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain","institution_ids":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111462730","display_name":"G. Pastor","orcid":null},"institutions":[{"id":"https://openalex.org/I134820265","display_name":"Consejo Superior de Investigaciones Cient\u00edficas","ror":"https://ror.org/02gfc7t72","country_code":"ES","type":"government","lineage":["https://openalex.org/I134820265"]},{"id":"https://openalex.org/I4210087408","display_name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n \u201cLeonardo Torres Quevedo\u201d","ror":"https://ror.org/00zsy6110","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"G. Pastor","raw_affiliation_strings":["Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain","institution_ids":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007038086","display_name":"Marius\u2010F. Danca","orcid":"https://orcid.org/0000-0001-7699-8709"},"institutions":[{"id":"https://openalex.org/I4210141787","display_name":"Romanian Institute of Science and Technology","ror":"https://ror.org/04dchsd96","country_code":"RO","type":"nonprofit","lineage":["https://openalex.org/I4210141787"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"M.-F. Danca","raw_affiliation_strings":["Romanian Institute of Science and Technology, Cire\u015filor 29, Cluj-Napoca 400487, Rom\u00e2nia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Romanian Institute of Science and Technology, Cire\u015filor 29, Cluj-Napoca 400487, Rom\u00e2nia","institution_ids":["https://openalex.org/I4210141787"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061746772","display_name":"A. Mart\u00edn","orcid":"https://orcid.org/0000-0003-0828-3669"},"institutions":[{"id":"https://openalex.org/I134820265","display_name":"Consejo Superior de Investigaciones Cient\u00edficas","ror":"https://ror.org/02gfc7t72","country_code":"ES","type":"government","lineage":["https://openalex.org/I134820265"]},{"id":"https://openalex.org/I4210087408","display_name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n \u201cLeonardo Torres Quevedo\u201d","ror":"https://ror.org/00zsy6110","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Martin","raw_affiliation_strings":["Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"],"raw_orcid":"https://orcid.org/0000-0003-0828-3669","affiliations":[{"raw_affiliation_string":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain","institution_ids":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058528777","display_name":"Amalia B. Or\u00fae","orcid":"https://orcid.org/0000-0002-4422-5004"},"institutions":[{"id":"https://openalex.org/I134820265","display_name":"Consejo Superior de Investigaciones Cient\u00edficas","ror":"https://ror.org/02gfc7t72","country_code":"ES","type":"government","lineage":["https://openalex.org/I134820265"]},{"id":"https://openalex.org/I4210087408","display_name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n \u201cLeonardo Torres Quevedo\u201d","ror":"https://ror.org/00zsy6110","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. B. Orue","raw_affiliation_strings":["Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain","institution_ids":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087010650","display_name":"F. Montoya","orcid":"https://orcid.org/0000-0002-8817-8705"},"institutions":[{"id":"https://openalex.org/I134820265","display_name":"Consejo Superior de Investigaciones Cient\u00edficas","ror":"https://ror.org/02gfc7t72","country_code":"ES","type":"government","lineage":["https://openalex.org/I134820265"]},{"id":"https://openalex.org/I4210087408","display_name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n \u201cLeonardo Torres Quevedo\u201d","ror":"https://ror.org/00zsy6110","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"F. Montoya","raw_affiliation_strings":["Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain","institution_ids":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033193694","display_name":"Luis Hern\u00e1ndez Encinas","orcid":"https://orcid.org/0000-0001-6980-2683"},"institutions":[{"id":"https://openalex.org/I134820265","display_name":"Consejo Superior de Investigaciones Cient\u00edficas","ror":"https://ror.org/02gfc7t72","country_code":"ES","type":"government","lineage":["https://openalex.org/I134820265"]},{"id":"https://openalex.org/I4210087408","display_name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n \u201cLeonardo Torres Quevedo\u201d","ror":"https://ror.org/00zsy6110","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"L. Hern\u00e1ndez Encinas","raw_affiliation_strings":["Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain","institution_ids":["https://openalex.org/I134820265","https://openalex.org/I4210087408"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050763177","display_name":"Emanuel \u021aundrea","orcid":"https://orcid.org/0000-0002-1315-3159"},"institutions":[{"id":"https://openalex.org/I4210115364","display_name":"Emanuel University","ror":"https://ror.org/02aayd667","country_code":"RO","type":"education","lineage":["https://openalex.org/I4210115364"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"E. \u0162undrea","raw_affiliation_strings":["Emanuel University of Oradea, Nuf\u01cerului 87, 410597, Oradea, Rom\u00e2nia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Emanuel University of Oradea, Nuf\u01cerului 87, 410597, Oradea, Rom\u00e2nia","institution_ids":["https://openalex.org/I4210115364"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.066,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.74624686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"28","issue":"05","first_page":"1850065","last_page":"1850065"},"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":0.994700014591217,"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":0.994700014591217,"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":0.988099992275238,"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/T10244","display_name":"Chaos control and synchronization","score":0.9873999953269958,"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/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.827988862991333},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7506343126296997},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7367246150970459},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6918792724609375},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.6883573532104492},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.5561493635177612},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.4879400432109833},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.4621046483516693},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.4478147029876709},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34606051445007324},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32289451360702515},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3217812776565552},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14142921566963196},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11363285779953003}],"concepts":[{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.827988862991333},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7506343126296997},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7367246150970459},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6918792724609375},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.6883573532104492},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.5561493635177612},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.4879400432109833},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.4621046483516693},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.4478147029876709},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34606051445007324},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32289451360702515},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3217812776565552},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14142921566963196},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11363285779953003},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127418500657","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418500657","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313831","display_name":"Comunidad de Madrid","ror":null},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1602853338","https://openalex.org/W1900024119","https://openalex.org/W1992769224","https://openalex.org/W2008624415","https://openalex.org/W2011900287","https://openalex.org/W2046141712","https://openalex.org/W2066452473","https://openalex.org/W2102892532","https://openalex.org/W2300229942","https://openalex.org/W3098784191","https://openalex.org/W3123180672"],"related_works":["https://openalex.org/W1518155199","https://openalex.org/W2803928976","https://openalex.org/W4225624922","https://openalex.org/W4366139701","https://openalex.org/W3215350949","https://openalex.org/W2404180431","https://openalex.org/W2361894068","https://openalex.org/W4245057904","https://openalex.org/W4318218315","https://openalex.org/W2805247396"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"a":[3,11,60,76],"conjecture":[4,20,40],"to":[5,30,38],"draw":[6],"the":[7,33,39,43,79],"bifurcation":[8,34,64],"diagram":[9],"of":[10,82],"map":[12,61,77],"with":[13,54,62,78],"multiple":[14],"critical":[15],"points":[16],"is":[17,21],"enunciated.":[18],"The":[19],"checked":[22],"by":[23,48,72],"using":[24],"two":[25],"quartic":[26],"maps":[27,53],"in":[28],"order":[29],"verify":[31],"that":[32,59],"diagrams":[35],"obtained":[36],"according":[37],"contain":[41],"all":[42],"periodic":[44,67],"orbits":[45,68],"previously":[46],"counted":[47,71],"Xie":[49],"and":[50],"Hao":[51],"for":[52,75],"four":[55],"laps.":[56,83],"We":[57],"show":[58],"split":[63],"contains":[65],"more":[66],"than":[69],"those":[70],"these":[73],"authors":[74],"same":[80],"number":[81]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
