{"id":"https://openalex.org/W2003806501","doi":"https://doi.org/10.1088/0951-7715/25/7/1981","title":"Circle diffeomorphisms: quasi-reducibility and commuting diffeomorphisms","display_name":"Circle diffeomorphisms: quasi-reducibility and commuting diffeomorphisms","publication_year":2012,"publication_date":"2012-06-13","ids":{"openalex":"https://openalex.org/W2003806501","doi":"https://doi.org/10.1088/0951-7715/25/7/1981","mag":"2003806501"},"language":"en","primary_location":{"id":"doi:10.1088/0951-7715/25/7/1981","doi":"https://doi.org/10.1088/0951-7715/25/7/1981","is_oa":false,"landing_page_url":"https://doi.org/10.1088/0951-7715/25/7/1981","pdf_url":null,"source":{"id":"https://openalex.org/S158842918","display_name":"Nonlinearity","issn_l":"0951-7715","issn":["0951-7715","1361-6544"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nonlinearity","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00628298/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013283264","display_name":"Mostapha Benhenda","orcid":"https://orcid.org/0000-0002-7894-3696","observed_orcids":["https://orcid.org/0000-0002-7894-3696"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mostapha Benhenda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5013283264"],"corresponding_institution_ids":[],"apc_list":{"value":3325,"currency":"USD","value_usd":3325},"apc_paid":null,"fwci":0.3288,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.42752728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":93},"biblio":{"volume":"25","issue":"7","first_page":"1981","last_page":"1995"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9994999766349792,"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":0.9994999766349792,"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":0.0003000000142492354,"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/T11151","display_name":"Advanced Topology and Set 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/circle-diffeomorphisms","display_name":"circle diffeomorphisms","score":1.0},{"id":"https://openalex.org/keywords/rotation-number","display_name":"rotation number","score":0.8029999732971191},{"id":"https://openalex.org/keywords/baire-category-theorem","display_name":"Baire category theorem","score":0.6899999976158142},{"id":"https://openalex.org/keywords/irrational-rotation-number","display_name":"irrational rotation number","score":0.6399999856948853}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8904566764831543},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5234954953193665}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1088/0951-7715/25/7/1981","doi":"https://doi.org/10.1088/0951-7715/25/7/1981","is_oa":false,"landing_page_url":"https://doi.org/10.1088/0951-7715/25/7/1981","pdf_url":null,"source":{"id":"https://openalex.org/S158842918","display_name":"Nonlinearity","issn_l":"0951-7715","issn":["0951-7715","1361-6544"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nonlinearity","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00628298v4","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-00628298","pdf_url":"https://hal.science/hal-00628298/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2011","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.592.8174","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.592.8174","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/67/47/88/PDF/majtexdeuxpreamble.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00628298v4","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-00628298","pdf_url":"https://hal.science/hal-00628298/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2011","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2003806501.pdf","grobid_xml":"https://content.openalex.org/works/W2003806501.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W151658970","https://openalex.org/W191684985","https://openalex.org/W1610337337","https://openalex.org/W1975862088","https://openalex.org/W1981888620","https://openalex.org/W1994513039","https://openalex.org/W2004162357","https://openalex.org/W2021495611","https://openalex.org/W2028310036","https://openalex.org/W2036046498","https://openalex.org/W2069663696","https://openalex.org/W2095527902","https://openalex.org/W2133311994","https://openalex.org/W2312881186","https://openalex.org/W3216723540"],"related_works":["https://openalex.org/W7096322338","https://openalex.org/W2028310036","https://openalex.org/W1487334645","https://openalex.org/W48559738","https://openalex.org/W4301381646","https://openalex.org/W7098107688","https://openalex.org/W2074962916","https://openalex.org/W2055019266","https://openalex.org/W1973897537","https://openalex.org/W2665599022"],"abstract_inverted_index":{"In":[0,92],"this":[1,101],"article,":[2],"we":[3],"show":[4],"two":[5,58],"related":[6],"results":[7],"on":[8,15],"circle":[9],"diffeomorphisms.":[10],"The":[11,47],"first":[12],"result":[13,49],"is":[14,32,73,99,107,138],"quasi-reducibility:":[16],"for":[17,23,51,69],"a":[18,38,45,52],"Baire-dense":[19,53,102],"set":[20,54,121,142],"of":[21,27,55,78,122,143],"\u03b1,":[22,30,56],"any":[24],"diffeomorphism":[25],"f":[26,41,61,66],"rotation":[28,70,133,147],"number":[29,110],"it":[31,72,94],"possible":[33,74],"to":[34,75,90],"accumulate":[35],"R\u03b1":[36],"with":[37,128,132,146],"sequence":[39],"hn":[40,43],"h\u22121n,":[42],"being":[44],"diffeomorphism.":[46],"second":[48],"is:":[50],"given":[57],"commuting":[59,81,123,144],"diffeomorphisms":[60,82,124,145],"and":[62,84,104,131],"g,":[63],"such":[64,111],"that":[65,86,96,112],"has":[67],"\u03b1":[68,98],"number,":[71],"approach":[76],"each":[77],"them":[79],"by":[80],"fn":[83],"gn":[85],"are":[87,115],"differentiably":[88],"conjugated":[89],"rotations.":[91],"particular,":[93],"implies":[95],"if":[97,105],"in":[100,140],"set,":[103],"\u03b2":[106],"an":[108],"ir-rational":[109],"(\u03b1,":[113,135,149],"\u03b2)":[114,136],"not":[116],"simultaneously":[117],"Diophantine,":[118],"then":[119],"the":[120,141],"(":[125],"f,":[126],"g)":[127],"singular":[129],"conjugacy,":[130],"numbers":[134,148],"respectively,":[137],"C\u221e-dense":[139],"\u03b2).":[150],"1":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2025-10-10T00:00:00"}