{"id":"https://openalex.org/W2069773156","doi":"https://doi.org/10.1142/s0218127404010254","title":"ON A PARTICULAR FOLIATION ASSOCIATED WITH A POLYNOMIAL FAMILY OF NONINVERTIBLE MAPS OF THE PLANE","display_name":"ON A PARTICULAR FOLIATION ASSOCIATED WITH A POLYNOMIAL FAMILY OF NONINVERTIBLE MAPS OF THE PLANE","publication_year":2004,"publication_date":"2004-05-01","ids":{"openalex":"https://openalex.org/W2069773156","doi":"https://doi.org/10.1142/s0218127404010254","mag":"2069773156"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127404010254","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404010254","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/A5045586765","display_name":"Laura Gardini","orcid":"https://orcid.org/0000-0002-3386-6543"},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"education","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"LAURA GARDINI","raw_affiliation_strings":["Istituto di Scienze Economiche, University of Urbino, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto di Scienze Economiche, University of Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033752892","display_name":"Ilaria Foroni","orcid":"https://orcid.org/0000-0002-5296-531X"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"ILARIA FORONI","raw_affiliation_strings":["University Bicocca, Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University Bicocca, Milano, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108428626","display_name":"Christian Mira","orcid":null},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"education","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"CHRISTIAN MIRA","raw_affiliation_strings":["19 rue d'Occitanie, 31130 Quint Fonsegrives, France","Istituto di Scienze Economiche, University of Urbino, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"19 rue d'Occitanie, 31130 Quint Fonsegrives, France","institution_ids":[]},{"raw_affiliation_string":"Istituto di Scienze Economiche, University of Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.15368091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"05","first_page":"1601","last_page":"1624"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9854000210762024,"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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9854000210762024,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9815000295639038,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9753000140190125,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/foliation","display_name":"Foliation (geology)","score":0.7571754455566406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7410248517990112},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6167992353439331},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5666242241859436},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.49692466855049133},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37143605947494507},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.32725876569747925},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.09176596999168396}],"concepts":[{"id":"https://openalex.org/C168425004","wikidata":"https://www.wikidata.org/wiki/Q525802","display_name":"Foliation (geology)","level":3,"score":0.7571754455566406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7410248517990112},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6167992353439331},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5666242241859436},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.49692466855049133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37143605947494507},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32725876569747925},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.09176596999168396},{"id":"https://openalex.org/C26687426","wikidata":"https://www.wikidata.org/wiki/Q47069","display_name":"Metamorphic rock","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127404010254","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404010254","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:boa.unimib.it:10281/3632","is_oa":false,"landing_page_url":"http://hdl.handle.net/10281/3632","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.5699999928474426,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1597461812","https://openalex.org/W1974302683","https://openalex.org/W1980137179","https://openalex.org/W2014537461","https://openalex.org/W2044646393","https://openalex.org/W2070830204","https://openalex.org/W2078010300","https://openalex.org/W2087934695","https://openalex.org/W4292510609"],"related_works":["https://openalex.org/W2008800481","https://openalex.org/W2069687362","https://openalex.org/W2002994501","https://openalex.org/W2028108558","https://openalex.org/W1989920940","https://openalex.org/W2133497138","https://openalex.org/W4210984194","https://openalex.org/W2091544531","https://openalex.org/W2951867858","https://openalex.org/W2018134948"],"abstract_inverted_index":{"The":[0,43,91,180,215],"present":[1,191],"work":[2],"describes":[3],"a":[4,75,85,99,108,176,192,197,204,208,221],"family":[5,94,184],"of":[6,10,58,69,88,102,155,182,199,217,234],"polynomial":[7],"noninvertible":[8],"maps":[9,93,181],"the":[11,53,89,103,112,115,132,138,143,165,183,200,218,232,240,244,250],"plane":[12,76],"shared":[13],"within":[14],"two":[15,40,61,70,122,133],"open":[16],"regions:":[17],"(i)":[18],"(denoted":[19,32],"by":[20,33,52],"Z":[21,34,45,48,64,117,228],"0":[22,46],")":[23,36],"each":[24,37,81],"point":[25,38],"having":[26,39,60,157],"no":[27],"real":[28,41,160,235],"preimage,":[29],"and":[30,126,148],"(ii)":[31],"2":[35,49,65,118,125,147],"preimages.":[42,63],"regions":[44,227],",":[47],"are":[50],"separated":[51,120],"critical":[54],"curve":[55],"LC,":[56,80],"locus":[57],"points":[59,156],"coincident":[62],"is":[66,95,119,152],"made":[67,153],"up":[68,154],"sheets":[71],"(giving":[72],"rise":[73,174],"to":[74,175,238,249],"foliation)":[77],"joining":[78],"on":[79,207],"being":[82,168,231],"associated":[83],"with":[84],"well-defined":[86],"inverse":[87],"map.":[90,253],"considered":[92],"structurally":[96,223,251],"unstable.":[97],"For":[98],"wide":[100],"choice":[101],"parameter":[104,246],"space":[105],"it":[106,213],"generates":[107],"singular":[109],"foliation":[110,241],"in":[111],"sense":[113],"that":[114],"region":[116],"into":[121,220],"zones,":[123],"Z'":[124,146],"[Formula:":[127,149],"see":[128,150],"text],":[129],"inside":[130],"which":[131,194],"preimages":[134],"do":[135],"not":[136],"have":[137,185],"same":[139],"qualitative":[140],"behavior.":[141],"Moreover,":[142],"boundary":[144],"between":[145],"text]":[151],"only":[158],"one":[159,167],"preimage":[161],"at":[162,169],"finite":[163],"distance,":[164],"second":[166],"infinity.":[170],"This":[171,202],"situation":[172],"gives":[173],"nonclassical":[177],"homoclinic":[178],"bifurcation.":[179],"another":[186],"important":[187],"feature:":[188],"their":[189],"inverses":[190],"denominator":[193],"vanish":[195],"along":[196],"line":[198],"plane.":[201],"has":[203],"great":[205],"consequence":[206],"chaotic":[209],"attractor":[210],"structure,":[211],"when":[212,243],"exists.":[214],"imbedding":[216,245],"map":[219],"wider":[222],"stable":[224],"family,":[225],"generating":[226],"k":[229],"(k=1,3":[230],"number":[233],"preimages),":[236],"permits":[237],"understand":[239],"nature":[242],"cancels":[247],"leading":[248],"unstable":[252]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
