{"id":"https://openalex.org/W2167216476","doi":"https://doi.org/10.1112/jlms/jdt055","title":"Explosion of smoothness for conjugacies between multimodal maps","display_name":"Explosion of smoothness for conjugacies between multimodal maps","publication_year":2013,"publication_date":"2013-10-26","ids":{"openalex":"https://openalex.org/W2167216476","doi":"https://doi.org/10.1112/jlms/jdt055","mag":"2167216476"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdt055","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdt055","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1111.5554","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021650480","display_name":"Jos\u00e9 F. Alves","orcid":"https://orcid.org/0000-0001-9241-5198"},"institutions":[{"id":"https://openalex.org/I126158947","display_name":"Universidade Federal da Bahia","ror":"https://ror.org/03k3p7647","country_code":"BR","type":"education","lineage":["https://openalex.org/I126158947"]},{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I4210125590","display_name":"Institute for Systems Engineering and Computers","ror":"https://ror.org/033wn8m60","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210125590"]}],"countries":["BR","PT"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 F. Alves","raw_affiliation_strings":["Centro de Matema\u0301tica, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal, jfalves@fc.up.pt, http://www.fc.up.pt/cmup/jfalves","Departamento de Matem\u00e1tica, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil","INESC Porto LA e Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Matema\u0301tica, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal, jfalves@fc.up.pt, http://www.fc.up.pt/cmup/jfalves","institution_ids":["https://openalex.org/I182534213"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil","institution_ids":["https://openalex.org/I126158947"]},{"raw_affiliation_string":"INESC Porto LA e Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal","institution_ids":["https://openalex.org/I4210125590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103816293","display_name":"Vilton Pinheiro","orcid":null},"institutions":[{"id":"https://openalex.org/I126158947","display_name":"Universidade Federal da Bahia","ror":"https://ror.org/03k3p7647","country_code":"BR","type":"education","lineage":["https://openalex.org/I126158947"]},{"id":"https://openalex.org/I4210125590","display_name":"Institute for Systems Engineering and Computers","ror":"https://ror.org/033wn8m60","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210125590"]}],"countries":["BR","PT"],"is_corresponding":false,"raw_author_name":"Vilton Pinheiro","raw_affiliation_strings":["Departamento de Matema\u0301tica, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil, viltonj@ufba.br, http://www.pgmat.ufba.br","INESC Porto LA e Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal","Departamento de Matem\u00e1tica, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matema\u0301tica, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil, viltonj@ufba.br, http://www.pgmat.ufba.br","institution_ids":["https://openalex.org/I126158947"]},{"raw_affiliation_string":"INESC Porto LA e Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal","institution_ids":["https://openalex.org/I4210125590"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil","institution_ids":["https://openalex.org/I126158947"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030248292","display_name":"Alberto A. Pinto","orcid":"https://orcid.org/0000-0003-2953-6688"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I4210166615","display_name":"INESC TEC","ror":"https://ror.org/05fa8ka61","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210125590","https://openalex.org/I4210166615"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Alberto A. Pinto","raw_affiliation_strings":["LIAAD-INESC TEC e Departamento de Matema\u0301tica, Faculdade de Cie\u0302ncias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal, http://www.liaad.up.pt/people/researchers-ph.d./people/alberto-pinto-1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIAAD-INESC TEC e Departamento de Matema\u0301tica, Faculdade de Cie\u0302ncias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal, http://www.liaad.up.pt/people/researchers-ph.d./people/alberto-pinto-1","institution_ids":["https://openalex.org/I182534213","https://openalex.org/I4210166615"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030248292"],"corresponding_institution_ids":["https://openalex.org/I182534213","https://openalex.org/I4210166615"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.7944,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70327915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"89","issue":"1","first_page":"255","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991000294685364,"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/diffeomorphism","display_name":"Diffeomorphism","score":0.6592997312545776},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6312569379806519},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6159348487854004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5999963283538818},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5967262387275696},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.5428786873817444},{"id":"https://openalex.org/keywords/cusp","display_name":"Cusp (singularity)","score":0.5016272068023682},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4935671091079712},{"id":"https://openalex.org/keywords/periodic-point","display_name":"Periodic point","score":0.46348124742507935},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.46267861127853394},{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.45673561096191406},{"id":"https://openalex.org/keywords/renormalization","display_name":"Renormalization","score":0.4413056969642639},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43975886702537537},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3141263723373413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29852455854415894},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.17559286952018738},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1750001609325409}],"concepts":[{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.6592997312545776},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6312569379806519},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6159348487854004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5999963283538818},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5967262387275696},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.5428786873817444},{"id":"https://openalex.org/C2778400075","wikidata":"https://www.wikidata.org/wiki/Q655275","display_name":"Cusp (singularity)","level":2,"score":0.5016272068023682},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4935671091079712},{"id":"https://openalex.org/C46581059","wikidata":"https://www.wikidata.org/wiki/Q116301","display_name":"Periodic point","level":2,"score":0.46348124742507935},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.46267861127853394},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.45673561096191406},{"id":"https://openalex.org/C166124518","wikidata":"https://www.wikidata.org/wiki/Q1047702","display_name":"Renormalization","level":2,"score":0.4413056969642639},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43975886702537537},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3141263723373413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29852455854415894},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.17559286952018738},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1750001609325409}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1112/jlms/jdt055","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdt055","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1111.5554","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1111.5554","pdf_url":"https://arxiv.org/pdf/1111.5554","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.746.187","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.746.187","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1111.5554.pdf","raw_type":"text"},{"id":"pmh:oai:repositorio.inesctec.pt:123456789/3502","is_oa":true,"landing_page_url":"http://repositorio.inesctec.pt/handle/123456789/3502","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"","raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1111.5554","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1111.5554","pdf_url":"https://arxiv.org/pdf/1111.5554","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W63131501","https://openalex.org/W71948572","https://openalex.org/W109718719","https://openalex.org/W118740219","https://openalex.org/W148795238","https://openalex.org/W388910587","https://openalex.org/W650925811","https://openalex.org/W1480611223","https://openalex.org/W1500936776","https://openalex.org/W1520671517","https://openalex.org/W1521564611","https://openalex.org/W1531506108","https://openalex.org/W1677526569","https://openalex.org/W1770826890","https://openalex.org/W1914481674","https://openalex.org/W1964970632","https://openalex.org/W1978552647","https://openalex.org/W1980114330","https://openalex.org/W1983918081","https://openalex.org/W1989696488","https://openalex.org/W1998350389","https://openalex.org/W2002848328","https://openalex.org/W2007561358","https://openalex.org/W2010535610","https://openalex.org/W2019376501","https://openalex.org/W2019436220","https://openalex.org/W2033891755","https://openalex.org/W2034154786","https://openalex.org/W2036054716","https://openalex.org/W2040972198","https://openalex.org/W2050196610","https://openalex.org/W2065881298","https://openalex.org/W2074631999","https://openalex.org/W2078116828","https://openalex.org/W2084118311","https://openalex.org/W2087975981","https://openalex.org/W2090590722","https://openalex.org/W2097329148","https://openalex.org/W2100288792","https://openalex.org/W2124740519","https://openalex.org/W2130654662","https://openalex.org/W2146365798","https://openalex.org/W2166168812","https://openalex.org/W2748840121","https://openalex.org/W2922260991","https://openalex.org/W3162514650","https://openalex.org/W4239818894","https://openalex.org/W4250586217","https://openalex.org/W4302081698"],"related_works":["https://openalex.org/W4393106738","https://openalex.org/W2415945172","https://openalex.org/W4294596679","https://openalex.org/W2963700530","https://openalex.org/W2773692590","https://openalex.org/W2322135471","https://openalex.org/W2133777788","https://openalex.org/W2090154855","https://openalex.org/W2024382131","https://openalex.org/W4302193581"],"abstract_inverted_index":{"Let":[0],"f":[1,22],"and":[2,12,23,60,70],"g":[3,24,61],"be":[4],"smooth":[5,41],"multimodal":[6],"maps":[7,69],"with":[8],"no":[9,13],"periodic":[10],"attractors":[11],"neutral":[14],"points.":[15],"If":[16],"a":[17,28,40,49,75],"topological":[18],"conjugacy":[19],"h":[20,38,71,80],"between":[21],"is":[25,39,72,81],"C1":[26,73],"at":[27,74],"point":[29],"in":[30,43,83],"the":[31,44],"nearby":[32],"expanding":[33],"set":[34],"of":[35,46,48,52,77],"f,":[36],"then":[37,79],"diffeomorphism":[42],"basin":[45],"attraction":[47],"renormalization":[50],"interval":[51],"f.":[53],"In":[54],"particular,":[55],"if":[56],"f:I":[57],"\u2192":[58,64],"I":[59],":":[62],"J":[63,65],"are":[66],"Cr":[67,82],"unimodal":[68],"boundary":[76],"I,":[78],"I.":[84]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}