{"id":"https://openalex.org/W7117248385","doi":"https://doi.org/10.1002/mana.70293","title":"Generalized q\u2010Dimensions of Measures on Non\u2010Autonomous Conformal Sets","display_name":"Generalized q\u2010Dimensions of Measures on Non\u2010Autonomous Conformal Sets","publication_year":2026,"publication_date":"2026-10-30","ids":{"openalex":"https://openalex.org/W7117248385","doi":"https://doi.org/10.1002/mana.70293"},"language":"en","primary_location":{"id":"doi:10.1002/mana.70293","doi":"https://doi.org/10.1002/mana.70293","is_oa":false,"landing_page_url":"https://doi.org/10.1002/mana.70293","pdf_url":null,"source":{"id":"https://openalex.org/S73458468","display_name":"Mathematische Nachrichten","issn_l":"0025-584X","issn":["0025-584X","1522-2616"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-2"],"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":"Mathematische Nachrichten","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.19771","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080169504","display_name":"Jun Jie Miao","orcid":"https://orcid.org/0000-0002-8953-8995","observed_orcids":["https://orcid.org/0000-0002-8953-8995"]},"institutions":[{"id":"https://openalex.org/I204553293","display_name":"China University of Petroleum, Beijing","ror":"https://ror.org/041qf4r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I204553293"]},{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun Jie Miao","raw_affiliation_strings":["School of Mathematical Sciences Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP East China Normal University Shanghai China","School of Mathematics Physics and Artificial Intelligence China University of Petroleum\u2010Beijing Karamay China"],"raw_orcid":"https://orcid.org/0000-0002-8953-8995","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP East China Normal University Shanghai China","institution_ids":["https://openalex.org/I66867065"]},{"raw_affiliation_string":"School of Mathematics Physics and Artificial Intelligence China University of Petroleum\u2010Beijing Karamay China","institution_ids":["https://openalex.org/I204553293"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5121251961","display_name":"Tianrui Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianrui Wang","raw_affiliation_strings":["School of Mathematical Sciences Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP East China Normal University Shanghai China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP East China Normal University Shanghai China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080169504"],"corresponding_institution_ids":["https://openalex.org/I204553293","https://openalex.org/I66867065"],"apc_list":{"value":3460,"currency":"USD","value_usd":3460},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15841744,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":9.999999747378752e-05,"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/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/moran-sets","display_name":"Moran sets","score":0.8939999938011169},{"id":"https://openalex.org/keywords/iterated-function-systems","display_name":"iterated function systems","score":0.9860000014305115},{"id":"https://openalex.org/keywords/pressure-function","display_name":"pressure function","score":0.8140000104904175},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.7639999985694885},{"id":"https://openalex.org/keywords/bernoulli-measures","display_name":"Bernoulli measures","score":0.8009999990463257},{"id":"https://openalex.org/keywords/dimension-formula","display_name":"dimension formula","score":0.5339999794960022},{"id":"https://openalex.org/keywords/separation-conditions","display_name":"separation conditions","score":0.847000002861023}],"concepts":[{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.7976999878883362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.795199990272522},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6625000238418579},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5641999840736389},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.5602999925613403},{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.5126000046730042},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48910000920295715},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46129998564720154},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45260000228881836},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35589998960494995},{"id":"https://openalex.org/C3352285","wikidata":"https://www.wikidata.org/wiki/Q5422297","display_name":"Extremal length","level":4,"score":0.3513999879360199},{"id":"https://openalex.org/C54613284","wikidata":"https://www.wikidata.org/wiki/Q1191271","display_name":"Conformal field theory","level":3,"score":0.33869999647140503},{"id":"https://openalex.org/C164528419","wikidata":"https://www.wikidata.org/wiki/Q3042439","display_name":"Bernoulli scheme","level":3,"score":0.323199987411499},{"id":"https://openalex.org/C69151251","wikidata":"https://www.wikidata.org/wiki/Q846537","display_name":"Generalized function","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C173848574","wikidata":"https://www.wikidata.org/wiki/Q3507963","display_name":"Conformal symmetry","level":3,"score":0.3086000084877014},{"id":"https://openalex.org/C20167640","wikidata":"https://www.wikidata.org/wiki/Q5160243","display_name":"Conformal anomaly","level":4,"score":0.3084000051021576},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26019999384880066}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/mana.70293","doi":"https://doi.org/10.1002/mana.70293","is_oa":false,"landing_page_url":"https://doi.org/10.1002/mana.70293","pdf_url":null,"source":{"id":"https://openalex.org/S73458468","display_name":"Mathematische Nachrichten","issn_l":"0025-584X","issn":["0025-584X","1522-2616"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-2"],"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":"Mathematische Nachrichten","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2512.19771","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.19771","pdf_url":"https://arxiv.org/pdf/2512.19771","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.2512.19771","doi":"https://doi.org/10.48550/arxiv.2512.19771","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.19771","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:2512.19771","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.19771","pdf_url":"https://arxiv.org/pdf/2512.19771","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":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7117248385.pdf","grobid_xml":"https://content.openalex.org/works/W7117248385.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4404988659","https://openalex.org/W1987117445","https://openalex.org/W7097648878","https://openalex.org/W2111967675","https://openalex.org/W4415313353","https://openalex.org/W4403349345","https://openalex.org/W2572923720","https://openalex.org/W1967621996","https://openalex.org/W3112117113","https://openalex.org/W2074326293"],"abstract_inverted_index":{"ABSTRACT":[0],"The":[1],"generalized":[2,54,90,112,139],"\u2010dimension":[3,55,140],"of":[4,14,21,35,68,141,151,170],"a":[5,36,75,142],"measure":[6,16,144],"provides":[7],"information":[8],"both":[9],"on":[10,18,66],"the":[11,15,19,25,33,47,53,80,100,111,118,138,148,161,168,171,180,189],"multifractal":[12],"structure":[13],"and":[17,52,92,103,126,136,163,173,176],"dimension":[20,128],"its":[22,28],"support.":[23],"In":[24,59],"self\u2010conformal":[26],"setting,":[27],"value":[29],"is":[30,145],"obtained":[31],"from":[32,114],"zero":[34,150],"pressure":[37],"function,":[38],"but":[39],"non\u2010autonomous":[40,69,164],"attractors":[41,67],"carry":[42],"no":[43],"invariant":[44],"dynamics,":[45],"so":[46],"ergodic\u2010theoretic":[48],"tools":[49],"are":[50,124],"unavailable":[51],"may":[56],"not":[57],"exist.":[58],"this":[60,152],"paper,":[61],"we":[62,104,155],"study":[63],"measures":[64],"supported":[65],"conformal":[70],"iterated":[71],"function":[72],"systems":[73,135],"under":[74,117,188],"scale":[76,174,181],"condition":[77,182],"that":[78,106,179],"permits":[79],"minimum":[81],"contraction":[82],"ratios":[83],"to":[84,86,159,166,177],"tend":[85],"zero.":[87],"We":[88],"define":[89],"upper":[91],"lower":[93],"pressures":[94],"through":[95],"cut":[96],"sets":[97],"organized":[98],"by":[99,147],"geometric":[101],"scale,":[102],"prove":[105],"their":[107],"critical":[108],"values":[109],"bound":[110],"\u2010dimensions":[113],"above.":[115],"Moreover,":[116],"open":[119],"set":[120],"condition,":[121],"these":[122],"bounds":[123],"sharp":[125],"yield":[127],"formulae":[129],"for":[130],"every":[131],".":[132],"For":[133],"autonomous":[134,162],",":[137],"Gibbs":[143],"given":[146],"unique":[149],"pressure.":[153],"Finally,":[154],"provide":[156],"some":[157],"examples":[158],"illustrate":[160],"cases,":[165],"clarify":[167],"roles":[169],"separation":[172,191],"conditions,":[175],"show":[178],"cannot":[183],"be":[184],"dispensed":[185],"with":[186],"even":[187],"strong":[190],"condition.":[192]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-12-25T00:00:00"}
