{"id":"https://openalex.org/W629100739","doi":null,"title":"On perturbations of rational maps and construction of semiconjugacies on the Julia sets (Studies on complex dynamics and related topics)","display_name":"On perturbations of rational maps and construction of semiconjugacies on the Julia sets (Studies on complex dynamics and related topics)","publication_year":2001,"publication_date":"2001-07-01","ids":{"openalex":"https://openalex.org/W629100739","mag":"629100739"},"language":"en","primary_location":{"id":"pmh:oai:repository.kulib.kyoto-u.ac.jp:2433/41288","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2433/41288","pdf_url":"http://hdl.handle.net/2433/41288","source":{"id":"https://openalex.org/S4306401454","display_name":"Kyoto University Research Information Repository (Kyoto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I22299242","host_organization_name":"Kyoto University","host_organization_lineage":["https://openalex.org/I22299242"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Departmental Bulletin Paper"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2433/41288","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067057665","display_name":"Tomoki Kawahira","orcid":"https://orcid.org/0000-0003-0329-3892","observed_orcids":["https://orcid.org/0000-0003-0329-3892"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tomoki Kawahira","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0329-3892","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5067057665"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1220","issue":null,"first_page":"128","last_page":"140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":1.0,"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":1.0,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.0,"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"}},{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.0,"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-sets","display_name":"Julia sets","score":0.8679999709129333},{"id":"https://openalex.org/keywords/semi-conjugacy","display_name":"semi-conjugacy","score":0.7960000038146973},{"id":"https://openalex.org/keywords/dynamic-stability","display_name":"dynamic stability","score":0.8339999914169312},{"id":"https://openalex.org/keywords/fatou-set","display_name":"Fatou set","score":0.9800000190734863},{"id":"https://openalex.org/keywords/attracting-cycles","display_name":"attracting cycles","score":0.8330000042915344}],"concepts":[{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5824413895606995},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.5676878094673157},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.42722004652023315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39504826068878174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3698136806488037},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.3697465658187866},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.35790541768074036},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.34234797954559326},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2397438883781433},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.17370638251304626},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1116907000541687},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:repository.kulib.kyoto-u.ac.jp:2433/41288","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2433/41288","pdf_url":"http://hdl.handle.net/2433/41288","source":{"id":"https://openalex.org/S4306401454","display_name":"Kyoto University Research Information Repository (Kyoto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I22299242","host_organization_name":"Kyoto University","host_organization_lineage":["https://openalex.org/I22299242"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Departmental Bulletin Paper"},{"id":"mag:629100739","doi":null,"is_oa":false,"landing_page_url":"https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/41288/1/1220_11.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306549803","display_name":"\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u9332","issn_l":"1880-2818","issn":["1880-2818","2760-7046"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u9332","raw_type":null}],"best_oa_location":{"id":"pmh:oai:repository.kulib.kyoto-u.ac.jp:2433/41288","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2433/41288","pdf_url":"http://hdl.handle.net/2433/41288","source":{"id":"https://openalex.org/S4306401454","display_name":"Kyoto University Research Information Repository (Kyoto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I22299242","host_organization_name":"Kyoto University","host_organization_lineage":["https://openalex.org/I22299242"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Departmental Bulletin Paper"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W629100739.pdf","grobid_xml":"https://content.openalex.org/works/W629100739.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7095798522","https://openalex.org/W4232584779","https://openalex.org/W2033041133","https://openalex.org/W2096119743","https://openalex.org/W3128010357","https://openalex.org/W4414593205","https://openalex.org/W7101082189","https://openalex.org/W7131405891","https://openalex.org/W2316949068","https://openalex.org/W2018475118"],"abstract_inverted_index":{"In":[0],"this":[1,91,110,172],"note,":[2,111],"we":[3,48,112],"investigate":[4],"perturbations":[5,114],"of":[6,17,38,72,81,85,90,115,132,143,151,156,177,206],"parabolic":[7,26,42,58,120],"rational":[8,21,43,59,83,117,121,157],"maps":[9,60,84,158],"on":[10,52,99,134,146],"the":[11,34,79,96,100,104,129,135,147,175,182,204],"Riemann":[12],"sphere,":[13],"and":[14,77,127,165],"dynamical":[15,130],"stability":[16,131,142],"their":[18,53],"Julia":[19,54,136,148],"sets.A":[20],"map":[22,44,71,118],"$f$":[23,39,66,123,133,144,152],"is":[24,31,45,93,185,209],"called":[25],"if":[27],"every":[28],"critical":[29],"point":[30],"contained":[32],"in":[33],"Fatou":[35],"set.If":[36],"aperturbation":[37],"into":[40],"another":[41],"horocyclic,":[46],"then":[47,212],"can":[49],"construct":[50],"asemiconjugacy":[51],"sets.This":[55],"means":[56,153],"that":[57],"have":[61],"weak":[62],"J-stability":[63],"1J-stability":[64],"Let":[65],":":[67,161],"$\\hat{\\mathbb{C}}arrow\\hat{\\mathbb{C}}$":[68],"be":[69],"arational":[70],"degree":[73,86],"$d\\geq":[74],"2$":[75],",":[76,126],"$\\mathrm{R}\\mathrm{a}\\mathrm{t}_{d}$":[78],"space":[80,92],"all":[82],"$d$":[87],".The":[88],"topology":[89],"defined":[94],"by":[95,103],"uniform":[97],"convergence":[98],"sphere":[101],"measured":[102],"spherical":[105],"distance":[106],"$d_{\\sigma}(\\cdot,":[107],"\\cdot)$":[108],".In":[109],"discuss":[113],"a":[116,154,195],"(especially":[119],"map)":[122],"within":[124],"$\\mathrm{R}\\mathrm{a}\\mathrm{t}_{\\mathrm{d}}$":[125],"study":[128],"set":[137],"$J(f)$":[138],":That":[139],"is,":[140],"structural":[141],"restricted":[145],"set.Here":[149],"perturbation":[150],"family":[155,173],"$\\{f_{\\epsilon}\\in":[159],"\\mathrm{R}\\mathrm{a}\\mathrm{t}_{d}":[160],"\\epsilon\\in[0,1]\\}$":[162],"satisfying":[163],"$f_{0}=f$":[164],"$d_{\\sigma}(f_{\\epsilon},":[166],"f)arrow":[167],"\\mathrm{O}(\\epsilonarrow":[168],"0)$":[169],".We":[170],"represent":[171],"as":[174],"form":[176],"convergence,":[178],"$f_{\\epsilon}arrow":[179],"f$":[180],".Aboutthis,":[181],"result":[183],"below":[184],"famous:":[186],"Theorem":[187],"1.1":[188],"(":[189],"$\\mathrm{M}\\mathrm{a}\\tilde{\\mathrm{n}}\\acute{\\mathrm{e}}$":[190],"-Sad-Sullivan[10])1":[191],"If":[192],"f":[193],"has":[194],"connected":[196],"neighbor-":[197],"hood":[198],"U":[199],"$\\subset":[200],"\\mathrm{R}\\mathrm{a}\\mathrm{t}_{d}$":[201],"w":[202],"here":[203],"number":[205],"attracting":[207],"cycles":[208],"locally":[210],"constant,":[211]},"counts_by_year":[],"updated_date":"2026-08-31T07:19:18.363097","created_date":"2016-06-24T00:00:00"}
