{"id":"https://openalex.org/W2057909033","doi":"https://doi.org/10.1112/jlms/jdv002","title":"The Linear Fractional Model Theorem and Aleksandrov-Clark measures","display_name":"The Linear Fractional Model Theorem and Aleksandrov-Clark measures","publication_year":2015,"publication_date":"2015-03-13","ids":{"openalex":"https://openalex.org/W2057909033","doi":"https://doi.org/10.1112/jlms/jdv002","mag":"2057909033"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdv002","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdv002","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10138/155184","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082434592","display_name":"Eva A. Gallardo\u2010Guti\u00e9rrez","orcid":"https://orcid.org/0000-0002-6036-6800"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]},{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Eva A. Gallardo-Guti\u00e9rrez","raw_affiliation_strings":["Dpto. de Ana\u0301lisis Matema\u0301tico, Facultad de Matema\u0301ticas, Universidad Complutense de Madrid e ICMAT, Plaza de Ciencias 3, 28040 Madrid, Spain","Dpto. de An\u00e1lisis Matem\u00e1ticoFacultad de Matem\u00e1ticasUniversidad Complutense de Madrid e ICMATPlaza de Ciencias 328040 MadridSpain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. de Ana\u0301lisis Matema\u0301tico, Facultad de Matema\u0301ticas, Universidad Complutense de Madrid e ICMAT, Plaza de Ciencias 3, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I121748325","https://openalex.org/I4210157032"]},{"raw_affiliation_string":"Dpto. de An\u00e1lisis Matem\u00e1ticoFacultad de Matem\u00e1ticasUniversidad Complutense de Madrid e ICMATPlaza de Ciencias 328040 MadridSpain","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085063339","display_name":"Pekka Nieminen","orcid":"https://orcid.org/0000-0001-5671-8685"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Pekka J. Nieminen","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Helsinki, Box 68, FI-00014 Helsinki, Finland, pjniemin@cc.helsinki.fi","Department of Mathematics and Statistics, University of Helsinki, Box 68, FI\u201000014 Helsinki, Finland, pjniemin@cc.helsinki.fi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Helsinki, Box 68, FI-00014 Helsinki, Finland, pjniemin@cc.helsinki.fi","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I2800229700"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Helsinki, Box 68, FI\u201000014 Helsinki, Finland, pjniemin@cc.helsinki.fi","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082434592"],"corresponding_institution_ids":["https://openalex.org/I121748325","https://openalex.org/I4210157032"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.488,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63997232,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"91","issue":"2","first_page":"596","last_page":"608"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":1.0,"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9995999932289124,"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/T11822","display_name":"Analytic and geometric function theory","score":0.9991999864578247,"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/mathematics","display_name":"Mathematics","score":0.8771282434463501},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6638404726982117},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6516294479370117},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6409363746643066},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5470781922340393},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.5119413137435913},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4866095781326294},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46431398391723633},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3794722557067871}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8771282434463501},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6638404726982117},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6516294479370117},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6409363746643066},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5470781922340393},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.5119413137435913},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4866095781326294},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46431398391723633},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3794722557067871}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1112/jlms/jdv002","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdv002","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:helda.helsinki.fi:10138/155184","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/155184","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:helda.helsinki.fi:10138/155184","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/155184","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W102351708","https://openalex.org/W1551756560","https://openalex.org/W1589135728","https://openalex.org/W1999981902","https://openalex.org/W2026678333","https://openalex.org/W2027536842","https://openalex.org/W2037612300","https://openalex.org/W2054072455","https://openalex.org/W2148740922","https://openalex.org/W2316071099","https://openalex.org/W2323624395","https://openalex.org/W2325359535","https://openalex.org/W2584692947","https://openalex.org/W2955652834","https://openalex.org/W4231466523","https://openalex.org/W4232926426","https://openalex.org/W4237760562","https://openalex.org/W4242413584","https://openalex.org/W4246967993","https://openalex.org/W4249065537","https://openalex.org/W4299318877","https://openalex.org/W6681813274","https://openalex.org/W6765402346"],"related_works":["https://openalex.org/W1973077274","https://openalex.org/W2041781647","https://openalex.org/W1985218657","https://openalex.org/W2136357364","https://openalex.org/W2094532370","https://openalex.org/W2029537334","https://openalex.org/W354597570","https://openalex.org/W1925861234","https://openalex.org/W2057909033","https://openalex.org/W2963496172"],"abstract_inverted_index":{"A":[0],"remarkable":[1],"result":[2],"by":[3],"Denjoy":[4],"and":[5,98],"Wolff":[6],"states":[7],"that":[8,66],"every":[9],"analytic":[10,81],"self-map":[11],"\u03c6":[12,39],"of":[13,19,36,79,83,106,117],"the":[14,20,34,68,71,80,104,107],"open":[15],"unit":[16],"disc":[17],"D":[18,84],"complex":[21],"plane,":[22],"except":[23],"an":[24,28],"elliptic":[25],"automorphism,":[26],"has":[27],"attractive":[29],"fixed":[30,54,64,91],"point":[31,55,65,75],"to":[32,111],"which":[33],"sequence":[35],"iterates":[37],"{":[38],"n":[40,42],"}":[41],"\u2a7e":[43],"1":[44],"converges":[45],"uniformly":[46],"on":[47],"compact":[48],"sets:":[49],"if":[50],"there":[51,59],"is":[52,60],"no":[53],"in":[56,114],"D,":[57],"then":[58],"a":[61,77],"unique":[62],"boundary":[63],"does":[67],"job,":[69],"called":[70],"Denjoy\u2013Wolff":[72],"point.":[73],"This":[74],"provides":[76],"classification":[78],"self-maps":[82],"into":[85],"four":[86],"types:":[87],"maps":[88,97,112],"with":[89],"interior":[90],"point,":[92],"hyperbolic":[93],"maps,":[94],"parabolic":[95,99],"automorphism":[96],"non-automorphism":[100],"maps.":[101],"We":[102],"determine":[103],"convergence":[105],"Aleksandrov\u2013Clark":[108],"measures":[109],"associated":[110],"falling":[113],"each":[115],"group":[116],"such":[118],"classification.":[119]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2016-06-24T00:00:00"}
