{"id":"https://openalex.org/W2006613543","doi":"https://doi.org/10.1142/s0218127403007734","title":"On Continuous Iteration Semigroups on the Circle","display_name":"On Continuous Iteration Semigroups on the Circle","publication_year":2003,"publication_date":"2003-07-01","ids":{"openalex":"https://openalex.org/W2006613543","doi":"https://doi.org/10.1142/s0218127403007734","mag":"2006613543"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127403007734","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403007734","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/A5058883525","display_name":"Marek Cezary Zdun","orcid":"https://orcid.org/0000-0002-8120-3154"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I172685059","display_name":"Uniwersytet Komisji Edukacji Narodowej w Krakowie","ror":"https://ror.org/030mz2444","country_code":"PL","type":"education","lineage":["https://openalex.org/I172685059"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"M. C. Zdun","raw_affiliation_strings":["Institute of Mathematics, Pedagogical University, Podchora\u017cych 2, 30-084 Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Pedagogical University, Podchora\u017cych 2, 30-084 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I172685059","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058883525"],"corresponding_institution_ids":["https://openalex.org/I172685059","https://openalex.org/I4210137370"],"apc_list":null,"apc_paid":null,"fwci":0.4956,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59529463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"07","first_page":"1903","last_page":"1909"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.9991000294685364,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9991000294685364,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9987999796867371,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/unit-circle","display_name":"Unit circle","score":0.8178005218505859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6873562335968018},{"id":"https://openalex.org/keywords/continuous-function","display_name":"Continuous function (set theory)","score":0.5047498941421509},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4949020743370056},{"id":"https://openalex.org/keywords/uniform-continuity","display_name":"Uniform continuity","score":0.4113740921020508},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4113403856754303},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3560468554496765},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3126722574234009},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.16063395142555237}],"concepts":[{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.8178005218505859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6873562335968018},{"id":"https://openalex.org/C2778199601","wikidata":"https://www.wikidata.org/wiki/Q5165476","display_name":"Continuous function (set theory)","level":3,"score":0.5047498941421509},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4949020743370056},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.4113740921020508},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4113403856754303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3560468554496765},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3126722574234009},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.16063395142555237},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127403007734","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403007734","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":[{"id":"https://metadata.un.org/sdg/10","score":0.49000000953674316,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W74321208","https://openalex.org/W83545623","https://openalex.org/W1570038676","https://openalex.org/W1576126224","https://openalex.org/W2008352403"],"related_works":["https://openalex.org/W4232243637","https://openalex.org/W1984371604","https://openalex.org/W2567734856","https://openalex.org/W2402986807","https://openalex.org/W4239669546","https://openalex.org/W3196412721","https://openalex.org/W2335767804","https://openalex.org/W2358708818","https://openalex.org/W3081631371","https://openalex.org/W2171064973"],"abstract_inverted_index":{"In":[0],"this":[1],"note":[2],"we":[3],"give":[4],"a":[5],"general":[6],"description":[7],"of":[8,14],"iteration":[9],"semigroups":[10],"[Formula:":[11,21,37],"see":[12,22,38],"text]":[13,23],"continuous":[15,34],"functions":[16],"on":[17],"the":[18,26],"unit":[19],"circle":[20],"such":[24],"that":[25],"mapping":[27],"t":[28,31],"\u21a6":[29],"F":[30],"(z)":[32],"is":[33],"for":[35],"every":[36],"text].":[39]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}