{"id":"https://openalex.org/W7213601454","doi":"https://doi.org/10.48550/arxiv.2609.20036","title":"Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps","display_name":"Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213601454","doi":"https://doi.org/10.48550/arxiv.2609.20036"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20036","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20036","pdf_url":"https://arxiv.org/pdf/2609.20036","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/2609.20036","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111136887","display_name":"Yuya Arima","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Arima, Yuya","raw_affiliation_strings":["Graduate School of Mathematics , Nagoya University , Furocho , Chikusaku , Nagoya , 464-8602 , JAPAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Mathematics , Nagoya University , Furocho , Chikusaku , Nagoya , 464-8602 , JAPAN","institution_ids":["https://openalex.org/I60134161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111136887"],"corresponding_institution_ids":["https://openalex.org/I60134161"],"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":1.0,"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":1.0,"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":0.0,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/birkhoff-averages","display_name":"Birkhoff averages","score":0.8410000205039978},{"id":"https://openalex.org/keywords/multifractal-analysis","display_name":"multifractal analysis","score":0.9639999866485596},{"id":"https://openalex.org/keywords/real-analyticity","display_name":"real analyticity","score":0.8500000238418579},{"id":"https://openalex.org/keywords/strict-monotonicity","display_name":"strict monotonicity","score":0.8629999756813049},{"id":"https://openalex.org/keywords/equilibrium-measure","display_name":"equilibrium measure","score":0.7039999961853027},{"id":"https://openalex.org/keywords/pressure-function","display_name":"pressure function","score":0.9430000185966492},{"id":"https://openalex.org/keywords/thermodynamic-formalism","display_name":"thermodynamic formalism","score":0.7670000195503235}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8216999769210815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8122000098228455},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6546000242233276},{"id":"https://openalex.org/C133905733","wikidata":"https://www.wikidata.org/wiki/Q2629238","display_name":"Multifractal system","level":3,"score":0.5992000102996826},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5885999798774719},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5511000156402588},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.4961000084877014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.477400004863739},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.46389999985694885},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.4104999899864197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3971000015735626},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.36090001463890076},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33329999446868896},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C119104473","wikidata":"https://www.wikidata.org/wiki/Q188910","display_name":"Carnot cycle","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C1911482","wikidata":"https://www.wikidata.org/wiki/Q854531","display_name":"Real analysis","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C130231550","wikidata":"https://www.wikidata.org/wiki/Q5189500","display_name":"Real-valued function","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20036","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20036","pdf_url":"https://arxiv.org/pdf/2609.20036","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.2609.20036","doi":"https://doi.org/10.48550/arxiv.2609.20036","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20036","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.20036","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20036","pdf_url":"https://arxiv.org/pdf/2609.20036","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":[{"id":"https://openalex.org/G5461959186","display_name":"\u4e8c\u6b21\u5199\u50cf\u65cf\u3068\u30ea\u30e3\u30d7\u30ce\u30d5\u975e\u6b63\u5247\u96c6\u5408","funder_award_id":"25KJ1382","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213601454.pdf","grobid_xml":"https://content.openalex.org/works/W7213601454.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415959326","https://openalex.org/W4407276090","https://openalex.org/W4416436481","https://openalex.org/W1949628468","https://openalex.org/W1950226805","https://openalex.org/W2594203795","https://openalex.org/W1563254223","https://openalex.org/W1995545638","https://openalex.org/W1968083197","https://openalex.org/W7099147115"],"abstract_inverted_index":{"In":[0],"this":[1,56],"paper,":[2],"we":[3,58],"study":[4],"the":[5,23,30,36,41,44,47,60,70,74,95,104,114,122],"multifractal":[6],"analysis":[7],"of":[8,29,40,64,73,103,118],"Birkhoff":[9,31,105],"averages":[10],"for":[11,93],"parabolic":[12,82],"rational":[13],"maps.":[14],"We":[15],"establish":[16],"a":[17,52,78,90,119,125],"conditional":[18,48,96],"variational":[19,49,97],"principle":[20,98],"and":[21,26,38,62,69,99,113,116],"prove":[22,59],"real":[24,71,109],"analyticity":[25,72],"strict":[27,111],"monotonicity":[28],"spectrum,":[32,106],"as":[33,35],"well":[34],"existence":[37,61,115],"uniqueness":[39,63,117],"measure":[42,68,120],"attaining":[43,121],"supremum":[45,123],"in":[46],"principle,":[50],"on":[51,77,124],"certain":[53,126],"region.":[54,127],"To":[55],"end,":[57],"an":[65],"expanding":[66],"equilibrium":[67],"pressure":[75],"function":[76],"suitable":[79],"domain.":[80],"For":[81],"systems,":[83],"our":[84],"approach":[85],"using":[86],"thermodynamic":[87],"formalism":[88],"provides":[89],"unified":[91],"framework":[92],"establishing":[94],"investigating":[100],"finer":[101],"properties":[102],"including":[107],"its":[108],"analyticity,":[110],"monotonicity,":[112]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-09-19T00:00:00"}