{"id":"https://openalex.org/W7212057267","doi":"https://doi.org/10.48550/arxiv.2609.06658","title":"Equidistribution Measures of infinite entropy for Transcendental Functions","display_name":"Equidistribution Measures of infinite entropy for Transcendental Functions","publication_year":2026,"publication_date":"2026-09-06","ids":{"openalex":"https://openalex.org/W7212057267","doi":"https://doi.org/10.48550/arxiv.2609.06658"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.06658","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06658","pdf_url":"https://arxiv.org/pdf/2609.06658","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/2609.06658","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005842996","display_name":"Leandro Arosio","orcid":"https://orcid.org/0000-0003-2904-4472","observed_orcids":["https://orcid.org/0000-0003-2904-4472"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arosio, Leandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015216242","display_name":"Anna Miriam Benini","orcid":"https://orcid.org/0000-0001-9014-5235","observed_orcids":["https://orcid.org/0000-0001-9014-5235"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benini, Anna Miriam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108611946","display_name":"John Erik Forn\u00e6ss","orcid":"https://orcid.org/0009-0008-8416-4788","observed_orcids":["https://orcid.org/0009-0008-8416-4788"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Forn\u00e6ss, John Erik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110425736","display_name":"Han Peters","orcid":"https://orcid.org/0000-0003-1693-9752","observed_orcids":["https://orcid.org/0000-0003-1693-9752"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peters, Han","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/equidistribution","display_name":"equidistribution","score":0.9120000004768372},{"id":"https://openalex.org/keywords/transcendental-dynamics","display_name":"transcendental dynamics","score":0.9779999852180481},{"id":"https://openalex.org/keywords/entire-functions","display_name":"entire functions","score":0.8270000219345093},{"id":"https://openalex.org/keywords/invariant-measures","display_name":"invariant measures","score":0.7390000224113464},{"id":"https://openalex.org/keywords/transfer-operator","display_name":"transfer operator","score":0.8980000019073486},{"id":"https://openalex.org/keywords/symbolic-dynamics","display_name":"symbolic dynamics","score":0.7319999933242798},{"id":"https://openalex.org/keywords/preimages","display_name":"preimages","score":0.5550000071525574},{"id":"https://openalex.org/keywords/periodic-points","display_name":"periodic points","score":0.9980000257492065},{"id":"https://openalex.org/keywords/wandering-domains","display_name":"wandering domains","score":0.9179999828338623},{"id":"https://openalex.org/keywords/julia-sets","display_name":"Julia sets","score":0.5809999704360962},{"id":"https://openalex.org/keywords/normality","display_name":"normality","score":0.6230000257492065},{"id":"https://openalex.org/keywords/irreducibility","display_name":"irreducibility","score":0.6549999713897705},{"id":"https://openalex.org/keywords/mixing-measures","display_name":"mixing measures","score":0.7210000157356262}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8895999789237976},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.7958999872207642},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.649399995803833},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5374000072479248},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5091000199317932},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.48829999566078186},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4876999855041504},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4569000005722046},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.4287000000476837},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42730000615119934},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.40400001406669617},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C89436406","wikidata":"https://www.wikidata.org/wiki/Q1544261","display_name":"Totally disconnected space","level":3,"score":0.3682999908924103},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C6128204","wikidata":"https://www.wikidata.org/wiki/Q847600","display_name":"Entire function","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C16101541","wikidata":"https://www.wikidata.org/wiki/Q1350838","display_name":"Symbolic dynamics","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.25600001215934753},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.25450000166893005},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.06658","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06658","pdf_url":"https://arxiv.org/pdf/2609.06658","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.2609.06658","doi":"https://doi.org/10.48550/arxiv.2609.06658","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.06658","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:2609.06658","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06658","pdf_url":"https://arxiv.org/pdf/2609.06658","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212057267.pdf","grobid_xml":"https://content.openalex.org/works/W7212057267.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2534729756","https://openalex.org/W3097143899"],"related_works":["https://openalex.org/W2978509082","https://openalex.org/W2032348285","https://openalex.org/W3097143899","https://openalex.org/W1596770069","https://openalex.org/W3212892684","https://openalex.org/W7080125047","https://openalex.org/W2050330376","https://openalex.org/W1985197506","https://openalex.org/W2277931422","https://openalex.org/W7135028581"],"abstract_inverted_index":{"In":[0,61,117,227],"the":[1,24,38,62,68,81,99,118,126,230,233,242],"1980s":[2],"Lyubich":[3],"and":[4,19,44,58,71,108,130,159,173,217],"Freire-Lopes-Ma\u00f1\u00e9":[5],"proved":[6],"that":[7,196],"for":[8,77,94,143],"any":[9],"rational":[10,42,59,231],"function":[11],"of":[12,27,37,40,55,125,150,162,168,177,180,191,211,224],"degree":[13],"d":[14],"\\geq":[15],"2,":[16],"both":[17],"preimages":[18,203],"periodic":[20,225],"points":[21],"equidistribute":[22,204],"to":[23,49,73,113,136,199,205,229],"unique":[25],"measure":[26,210],"maximal":[28],"entropy":[29],"log(d).":[30],"Their":[31],"results":[32],"provide":[33,141],"a":[34,160],"fundamental":[35],"understanding":[36],"dynamics":[39],"iterated":[41],"functions,":[43],"have":[45,85],"since":[46],"been":[47],"generalized":[48],"many":[50,247],"different":[51,92],"contexts,":[52],"including":[53],"classes":[54,149,193],"higher-dimensional":[56],"polynomial":[57],"maps.":[60,188],"current":[63],"paper":[64],"we":[65,121,185,194,220,235],"depart":[66],"from":[67],"algebraic":[69],"category":[70],"aim":[72],"prove":[74,195,222],"analogous":[75],"statements":[76],"transcendental":[78,100,151],"functions":[79],"in":[80,98],"complex":[82],"plane,":[83],"which":[84,132,184],"infinite":[86,212],"topological":[87],"entropy.":[88,213],"We":[89,140],"introduce":[90],"two":[91],"methods":[93],"constructing":[95],"invariant":[96,138,207],"measures":[97,234],"setting,":[101,232],"namely":[102],"via":[103,109],"embedded":[104],"symbolic":[105],"dynamical":[106],"systems":[107],"transfer":[110],"operators":[111],"associated":[112],"suitably":[114],"chosen":[115,201],"weights.":[116],"latter":[119],"case":[120],"isolate":[122],"three":[123,148],"properties":[124],"weights":[127,243],"-normality,":[128],"tightness,":[129],"irreducibility-":[131],"together":[133],"imply":[134],"convergence":[135],"an":[137,206],"measure.":[139],"examples":[142],"each":[144,190],"method,":[145],"given":[146],"by":[147,165,174,240],"entire":[152],"functions:":[153],"disjoint-type":[154,218],"maps,":[155,158],"strongly":[156],"polynomial-like":[157],"class":[161],"maps":[163,216,219],"inspired":[164],"Baker's":[166],"construction":[167,176],"multiply":[169],"connected":[170],"wandering":[171],"domains":[172],"Bishop's":[175],"Julia":[178],"sets":[179],"Hausdorff":[181],"dimension":[182],"1,":[183],"call":[186],"Baker-Bishop":[187,215],"For":[189,214],"these":[192],"with":[197],"respect":[198],"carefully":[200],"weights,":[202],"mixing":[208],"probability":[209],"also":[221],"equidistribution":[223],"points.":[226],"contrast":[228],"construct":[236],"are":[237],"not":[238],"unique:":[239],"varying":[241],"one":[244],"obtains":[245],"infinitely":[246],"distinct":[248],"measures.":[249]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
