{"id":"https://openalex.org/W2014732831","doi":"https://doi.org/10.1142/s0218127405013460","title":"DYNAMICS OF A FAMILY OF QUADRATIC MAPS IN THE QUATERNION SPACE","display_name":"DYNAMICS OF A FAMILY OF QUADRATIC MAPS IN THE QUATERNION SPACE","publication_year":2005,"publication_date":"2005-08-01","ids":{"openalex":"https://openalex.org/W2014732831","doi":"https://doi.org/10.1142/s0218127405013460","mag":"2014732831"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405013460","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013460","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/A5085511859","display_name":"Shizuo Nakane","orcid":"https://orcid.org/0000-0002-4793-1983"},"institutions":[{"id":"https://openalex.org/I31618427","display_name":"Tokyo Polytechnic University","ror":"https://ror.org/035kpke84","country_code":"JP","type":"education","lineage":["https://openalex.org/I31618427"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"SHIZUO NAKANE","raw_affiliation_strings":["Tokyo Polytechnic University, 1583 Iiyama, Atsugi, Kanagawa 243-0297, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokyo Polytechnic University, 1583 Iiyama, Atsugi, Kanagawa 243-0297, Japan","institution_ids":["https://openalex.org/I31618427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085511859"],"corresponding_institution_ids":["https://openalex.org/I31618427"],"apc_list":null,"apc_paid":null,"fwci":0.4069,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.56333059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"08","first_page":"2535","last_page":"2543"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9994000196456909,"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":0.9994000196456909,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13234","display_name":"advanced mathematical theories","score":0.9894000291824341,"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/mandelbrot-set","display_name":"Mandelbrot set","score":0.8894238471984863},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7385311722755432},{"id":"https://openalex.org/keywords/social-connectedness","display_name":"Social connectedness","score":0.7292656898498535},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.709011435508728},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6688295602798462},{"id":"https://openalex.org/keywords/julia-set","display_name":"Julia set","score":0.6471453905105591},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6090533137321472},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.492064893245697},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4495953619480133},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4106122553348541},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1419650912284851},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12327247858047485},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0896376371383667}],"concepts":[{"id":"https://openalex.org/C97519476","wikidata":"https://www.wikidata.org/wiki/Q257","display_name":"Mandelbrot set","level":3,"score":0.8894238471984863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7385311722755432},{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.7292656898498535},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.709011435508728},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6688295602798462},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.6471453905105591},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6090533137321472},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.492064893245697},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4495953619480133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4106122553348541},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1419650912284851},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12327247858047485},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0896376371383667},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127405013460","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013460","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1646303234","https://openalex.org/W2002332726","https://openalex.org/W2004495154","https://openalex.org/W2007774204","https://openalex.org/W2058123371","https://openalex.org/W4231967458","https://openalex.org/W4248287615"],"related_works":["https://openalex.org/W2372579255","https://openalex.org/W1972311046","https://openalex.org/W2169256438","https://openalex.org/W4308870400","https://openalex.org/W4391023542","https://openalex.org/W4382774916","https://openalex.org/W119062992","https://openalex.org/W4239801010","https://openalex.org/W2059491059","https://openalex.org/W2949360233"],"abstract_inverted_index":{"The":[0],"dynamics":[1],"of":[2,5,17,32],"a":[3],"family":[4,34],"quadratic":[6],"maps":[7],"in":[8],"the":[9,18,29,42],"quaternion":[10],"space":[11],"is":[12,22,26,35],"investigated.":[13],"In":[14],"particular,":[15],"connectivity":[16],"filled-in":[19],"Julia":[20],"sets":[21],"completely":[23,51],"determined.":[24],"It":[25],"shown":[27],"that":[28],"connectedness":[30],"locus":[31],"this":[33],"not":[36],"equal":[37],"to":[38],"what":[39],"we":[40],"call":[41],"quaternionic":[43],"Mandelbrot":[44],"set.":[45],"Hyperbolic":[46],"components":[47],"will":[48],"also":[49],"be":[50],"characterized.":[52]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}