{"id":"https://openalex.org/W1881499715","doi":"https://doi.org/10.1080/10586458.2015.1048011","title":"Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family","display_name":"Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family","publication_year":2015,"publication_date":"2015-12-04","ids":{"openalex":"https://openalex.org/W1881499715","doi":"https://doi.org/10.1080/10586458.2015.1048011","mag":"1881499715"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2015.1048011","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2015.1048011","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1504.00116","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044728356","display_name":"Ali Golmakani","orcid":null},"institutions":[{"id":"https://openalex.org/I79889768","display_name":"Universidade Federal de Alagoas","ror":"https://ror.org/00dna7t83","country_code":"BR","type":"education","lineage":["https://openalex.org/I79889768"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ali Golmakani","raw_affiliation_strings":["Universidade Federal de Alagoas, Macei\u00f3Alagoas, Brazil","Universidade Federal de Alagoas, Maceio, Alagoas, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Federal de Alagoas, Macei\u00f3Alagoas, Brazil","institution_ids":["https://openalex.org/I79889768"]},{"raw_affiliation_string":"Universidade Federal de Alagoas, Maceio, Alagoas, Brazil","institution_ids":["https://openalex.org/I79889768"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048855518","display_name":"Stefano Luzzatto","orcid":"https://orcid.org/0000-0001-6992-9190"},"institutions":[{"id":"https://openalex.org/I12323705","display_name":"The Abdus Salam International Centre for Theoretical Physics (ICTP)","ror":"https://ror.org/009gyvm78","country_code":"IT","type":"facility","lineage":["https://openalex.org/I12323705","https://openalex.org/I1286959531","https://openalex.org/I1293226324","https://openalex.org/I2801247003"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Luzzatto","raw_affiliation_strings":["Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy","Abdus Salam International Centre for Theoretical Physics, ICTP, Trieste, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy","institution_ids":["https://openalex.org/I12323705"]},{"raw_affiliation_string":"Abdus Salam International Centre for Theoretical Physics, ICTP, Trieste, Italy","institution_ids":["https://openalex.org/I12323705"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087872827","display_name":"Pawe\u0142 Pilarczyk","orcid":"https://orcid.org/0000-0003-0597-697X"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Pawe\u0142 Pilarczyk","raw_affiliation_strings":["Institute of Science and Technology Austria, Klosterneuburg, Austria","Institute of Science and Technology Austria, Klosterneuburg Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria, Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"Institute of Science and Technology Austria, Klosterneuburg Austria","institution_ids":["https://openalex.org/I157556583"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087872827"],"corresponding_institution_ids":["https://openalex.org/I157556583"],"apc_list":null,"apc_paid":null,"fwci":0.4788,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.59155738,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"2","first_page":"116","last_page":"124"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9994999766349792,"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":0.9994999766349792,"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/T10244","display_name":"Chaos control and synchronization","score":0.9836999773979187,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.98089998960495,"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/exponent","display_name":"Exponent","score":0.8487200140953064},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.8031187653541565},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7471034526824951},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6628996133804321},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.6199672818183899},{"id":"https://openalex.org/keywords/critical-exponent","display_name":"Critical exponent","score":0.6060748100280762},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6017825603485107},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.5086182355880737},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5022273063659668},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4669994115829468},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32038652896881104},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24029135704040527},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14142853021621704},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.10202538967132568},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07694557309150696},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07326284050941467}],"concepts":[{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.8487200140953064},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.8031187653541565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7471034526824951},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6628996133804321},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.6199672818183899},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.6060748100280762},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6017825603485107},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.5086182355880737},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5022273063659668},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4669994115829468},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32038652896881104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24029135704040527},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14142853021621704},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.10202538967132568},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07694557309150696},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07326284050941467},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.2015.1048011","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2015.1048011","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1504.00116","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.00116","pdf_url":"https://arxiv.org/pdf/1504.00116","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1504.00116","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.00116","pdf_url":"https://arxiv.org/pdf/1504.00116","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7200000286102295}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1984930436","https://openalex.org/W1985464051","https://openalex.org/W2007561358","https://openalex.org/W2008232244","https://openalex.org/W2010535610","https://openalex.org/W2011814687","https://openalex.org/W2022930709","https://openalex.org/W2028323882","https://openalex.org/W2034950660","https://openalex.org/W2036498947","https://openalex.org/W2036772106","https://openalex.org/W2042233505","https://openalex.org/W2043895765","https://openalex.org/W2047813281","https://openalex.org/W2070904005","https://openalex.org/W2076312407","https://openalex.org/W2103307614","https://openalex.org/W2124978857","https://openalex.org/W2139217731","https://openalex.org/W2144874394","https://openalex.org/W2333211228","https://openalex.org/W3102295883","https://openalex.org/W4249957515"],"related_works":["https://openalex.org/W4390962471","https://openalex.org/W3106283477","https://openalex.org/W3127252294","https://openalex.org/W2093110000","https://openalex.org/W193248292","https://openalex.org/W2951852385","https://openalex.org/W1598546354","https://openalex.org/W2559080656","https://openalex.org/W1963605683","https://openalex.org/W4213238192"],"abstract_inverted_index":{"We":[0,33,100],"use":[1],"rigorous":[2],"numerical":[3,62],"techniques":[4],"to":[5,64],"compute":[6,35,84],"a":[7,16,36,85],"lower":[8,86],"bound":[9,87],"for":[10,22,60,78,88,93],"the":[11,19,30,39,44,69,81,95,104,107,110,125,128,131],"exponent":[12,71],"of":[13,18,24,26,38,80,106,115,124,130],"expansivity":[14,70,90,111],"outside":[15,42,72],"neighborhood":[17,41,74],"critical":[20,40],"point":[21],"thousands":[23],"intervals":[25],"parameter":[27],"values":[28],"in":[29,66,97],"quadratic":[31],"family.":[32],"first":[34],"radius":[37,50],"which":[43],"map":[45],"is":[46,51,75],"uniformly":[47],"expanding.":[48],"This":[49],"taken":[52],"as":[53,55],"small":[54],"possible,":[56],"yet":[57],"large":[58],"enough":[59],"our":[61,116],"procedure":[63],"succeed":[65],"proving":[67],"that":[68,98],"this":[73,89],"positive.":[76],"Then,":[77],"each":[79],"intervals,":[82],"we":[83],"exponent,":[91],"valid":[92],"all":[94],"parameters":[96],"interval.":[99],"illustrate":[101],"and":[102,109,127],"study":[103],"distribution":[105],"radii":[108],"exponents.":[112],"The":[113,121],"results":[114,129],"computations":[117,132],"are":[118,133],"mathematically":[119],"rigorous.":[120],"source":[122],"code":[123],"software":[126],"made":[134],"publicly":[135],"available":[136],"at":[137],"http://www.pawelpilarczyk.com/quadratic/.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2016-06-24T00:00:00"}