{"id":"https://openalex.org/W2058251174","doi":"https://doi.org/10.1080/10586458.1993.10504569","title":"Dynamics of Certain Nonconformal Degree-Two Maps of the Plane","display_name":"Dynamics of Certain Nonconformal Degree-Two Maps of the Plane","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W2058251174","doi":"https://doi.org/10.1080/10586458.1993.10504569","mag":"2058251174"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.1993.10504569","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1993.10504569","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"],"host_organization_lineage_names":["Taylor & Francis"],"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":["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/A5000007083","display_name":"Ben Bielefeld","orcid":null},"institutions":[{"id":"https://openalex.org/I130440993","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32","country_code":"US","type":"government","lineage":["https://openalex.org/I130440993","https://openalex.org/I1330347796"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ben Bielefeld","raw_affiliation_strings":["Mathematics Department , National Security Agency , Ft. George G. Meade , MD , 20755"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department , National Security Agency , Ft. George G. Meade , MD , 20755","institution_ids":["https://openalex.org/I130440993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070397521","display_name":"Scott Sutherland","orcid":"https://orcid.org/0000-0001-9129-3344"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott Sutherland","raw_affiliation_strings":["Institute for Mathematical Sciences, State University of New York at Stony Brook , Stony Brook , NY , 11794-3660 E-mail: scott@math.sunysb.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematical Sciences, State University of New York at Stony Brook , Stony Brook , NY , 11794-3660 E-mail: scott@math.sunysb.edu","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030008307","display_name":"F. M. Tangerman","orcid":null},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Folkert Tangerman","raw_affiliation_strings":["Center for Advanced Manufacturing, Department of Applied Mathematics and Statistics , State University of New York at Stony Brook , Stony Brook , NY , 11794 E-mail: tangerma@ams.sunysb.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Advanced Manufacturing, Department of Applied Mathematics and Statistics , State University of New York at Stony Brook , Stony Brook , NY , 11794 E-mail: tangerma@ams.sunysb.edu","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059241473","display_name":"J. J. P. Veerman","orcid":"https://orcid.org/0000-0003-4551-5908"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"J. J. P. Veerman","raw_affiliation_strings":["Departamento de Matem\u00e1tica , Universidade Federal de Pernambuco, Cidade Universitaria , Rua Prof. Luis Freire, Recife , PE , 50740-540 , Brazil E-mail: veerman@dmat.ufpe.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica , Universidade Federal de Pernambuco, Cidade Universitaria , Rua Prof. Luis Freire, Recife , PE , 50740-540 , Brazil E-mail: veerman@dmat.ufpe.br","institution_ids":["https://openalex.org/I25112270"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.21761219,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2","issue":"4","first_page":"281","last_page":"300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9998000264167786,"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":0.9998000264167786,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9933000206947327,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/julia-set","display_name":"Julia set","score":0.919201135635376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8985381126403809},{"id":"https://openalex.org/keywords/mandelbrot-set","display_name":"Mandelbrot set","score":0.8929414749145508},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7027735114097595},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.634442925453186},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.5679386854171753},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5655009746551514},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5519834160804749},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.5220882296562195},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5084646940231323},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49819517135620117},{"id":"https://openalex.org/keywords/periodic-point","display_name":"Periodic point","score":0.47648924589157104},{"id":"https://openalex.org/keywords/open-set","display_name":"Open set","score":0.4692031741142273},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45366743206977844},{"id":"https://openalex.org/keywords/complex-quadratic-polynomial","display_name":"Complex quadratic polynomial","score":0.4232252240180969},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3920251727104187},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3382120132446289},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3316909074783325},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18239012360572815},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.13548621535301208}],"concepts":[{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.919201135635376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8985381126403809},{"id":"https://openalex.org/C97519476","wikidata":"https://www.wikidata.org/wiki/Q257","display_name":"Mandelbrot set","level":3,"score":0.8929414749145508},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7027735114097595},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.634442925453186},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.5679386854171753},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5655009746551514},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5519834160804749},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.5220882296562195},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5084646940231323},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49819517135620117},{"id":"https://openalex.org/C46581059","wikidata":"https://www.wikidata.org/wiki/Q116301","display_name":"Periodic point","level":2,"score":0.47648924589157104},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.4692031741142273},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45366743206977844},{"id":"https://openalex.org/C6077466","wikidata":"https://www.wikidata.org/wiki/Q5156597","display_name":"Complex quadratic polynomial","level":3,"score":0.4232252240180969},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3920251727104187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3382120132446289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3316909074783325},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18239012360572815},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.13548621535301208},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.1993.10504569","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1993.10504569","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"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W113739728","https://openalex.org/W390053422","https://openalex.org/W1514537983","https://openalex.org/W1525817413","https://openalex.org/W1561974326","https://openalex.org/W1570577480","https://openalex.org/W1601948230","https://openalex.org/W1612551514","https://openalex.org/W1646303234","https://openalex.org/W1900926888","https://openalex.org/W1968862828","https://openalex.org/W1979684610","https://openalex.org/W1988037432","https://openalex.org/W2023143345","https://openalex.org/W2035695789","https://openalex.org/W2062985118","https://openalex.org/W2141111991","https://openalex.org/W3138265894","https://openalex.org/W4239981491","https://openalex.org/W4251981560","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2094347864","https://openalex.org/W2370909541","https://openalex.org/W2059491059","https://openalex.org/W1972311046","https://openalex.org/W4382774916","https://openalex.org/W2390131699","https://openalex.org/W2997721922","https://openalex.org/W858532871","https://openalex.org/W2952748673","https://openalex.org/W4239801010"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,36,54,57,61,74,78,85,102,105],"rational":[3],"maps":[4],"given":[5],"by":[6],"z":[7,14],"|Z|2\u03b1\u20132":[8],"Z":[9],"2":[10],"+":[11],"c,":[12],"for":[13,39,45,63,81,90,108],"and":[15,18,23,77],"c":[16],"complex":[17],"\u03b1":[19,27,46,64,82,118],">":[20],"\u00bd":[21],"fixed":[22],"real.":[24],"The":[25],"case":[26,42],"=":[28],"1":[29,84],"corresponds":[30],"to":[31],"quadratic":[32],"polynomials:":[33],"some":[34],"of":[35,67,94,96,104],"well-known":[37],"results":[38],"this":[40,109],"conformal":[41],"still":[43],"hold":[44],"near":[47],"1,":[48,66],"while":[49],"others":[50],"break":[51],"down.":[52],"Among":[53],"differences":[55],"between":[56],"two":[58],"cases":[59],"are":[60],"possibility,":[62],"<":[65,83],"periodic":[68],"attractors":[69],"that":[70,80,101],"do":[71],"not":[72,114],"attract":[73],"critical":[75],"point,":[76],"fact":[79],"Julia":[86],"set":[87,93,107],"is":[88,111],"smooth":[89],"an":[91],"open":[92],"values":[95],"c.":[97],"Numerical":[98],"evidence":[99],"suggests":[100],"analogue":[103],"Mandelbrot":[106],"family":[110],"connected,":[112],"but":[113],"locally":[115],"connected":[116],"if":[117],"\u2260":[119],"1.":[120]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}