{"id":"https://openalex.org/W7223262456","doi":"https://doi.org/10.48550/arxiv.2610.30750","title":"On $C^2$ circle diffeomorphisms with rotation numbers of constant type","display_name":"On $C^2$ circle diffeomorphisms with rotation numbers of constant type","publication_year":2026,"publication_date":"2026-10-22","ids":{"openalex":"https://openalex.org/W7223262456","doi":"https://doi.org/10.48550/arxiv.2610.30750"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.30750","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30750","pdf_url":"https://arxiv.org/pdf/2610.30750","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.30750","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159317226","display_name":"Junhao Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Junhao","raw_affiliation_strings":["School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159313262","display_name":"Lin Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Lin","raw_affiliation_strings":["School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.00019999999494757503,"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":0.9980000257492065},{"id":"https://openalex.org/keywords/baire-category-theorem","display_name":"Baire category theorem","score":0.6909999847412109},{"id":"https://openalex.org/keywords/besov-spaces","display_name":"Besov spaces","score":0.6830000281333923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8634999990463257},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.7878999710083008},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.7300000190734863},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.666100025177002},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5979999899864197},{"id":"https://openalex.org/C135007989","wikidata":"https://www.wikidata.org/wiki/Q643156","display_name":"Rotation number","level":3,"score":0.5939000248908997},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.583299994468689},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5648000240325928},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5529000163078308},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4968999922275543},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.49309998750686646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37599998712539673},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C88977231","wikidata":"https://www.wikidata.org/wiki/Q681406","display_name":"Euler's rotation theorem","level":3,"score":0.25429999828338623},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.30750","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30750","pdf_url":"https://arxiv.org/pdf/2610.30750","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.30750","doi":"https://doi.org/10.48550/arxiv.2610.30750","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.30750","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.30750","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30750","pdf_url":"https://arxiv.org/pdf/2610.30750","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223262456.pdf","grobid_xml":"https://content.openalex.org/works/W7223262456.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1594572592","https://openalex.org/W4308242919","https://openalex.org/W4380853761"],"related_works":["https://openalex.org/W4297636848","https://openalex.org/W2027960302","https://openalex.org/W2095976469","https://openalex.org/W4315431289","https://openalex.org/W1985565866","https://openalex.org/W2010336548","https://openalex.org/W2896830725","https://openalex.org/W2571035105","https://openalex.org/W4413859838","https://openalex.org/W1590960325"],"abstract_inverted_index":{"For":[0],"every":[1,10],"irrational":[2],"rotation":[3,24],"number":[4],"$\u03b1$":[5],"of":[6,76],"constant":[7],"type":[8],"and":[9,30,56,62,86],"$q>1$,":[11],"we":[12],"construct":[13],"a":[14],"$C^2$":[15,29,77],"circle":[16],"diffeomorphism":[17],"$F$":[18],"arbitrarily":[19],"close":[20],"to":[21],"the":[22,27,50,53,73],"rigid":[23],"$R_\u03b1$":[25],"in":[26,52],"combined":[28],"$B^2_{2,q}$":[31],"topology":[32],"whose":[33],"normalized":[34],"conjugacy":[35,81],"is":[36],"not":[37],"Lipschitz.":[38],"We":[39],"also":[40],"prove":[41],"that":[42],"$F''\\in":[43],"B^0_{2,1}$":[44],"implies":[45],"global":[46],"$C^1$":[47,80],"conjugacy.":[48,91],"Thus":[49],"thresholds":[51],"Besov":[54],"summability":[55],"weak":[57],"Dini":[58],"scales":[59],"are":[60],"$q=1$":[61],"$\u03b3=1/2$,":[63],"respectively.":[64],"These":[65],"results":[66],"complement":[67],"Herman's":[68],"Baire":[69],"category":[70],"theorem":[71],"on":[72],"residual":[74],"existence":[75],"diffeomorphisms":[78],"without":[79],"by":[82],"providing":[83],"quantitative":[84],"counterexamples":[85],"sufficient":[87],"conditions":[88],"for":[89],"differentiable":[90]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-24T00:00:00"}
