{"id":"https://openalex.org/W2165735494","doi":"https://doi.org/10.1112/jlms/jds060","title":"Erd\u00f6s\u2013R\u00e9nyi laws for dynamical systems","display_name":"Erd\u00f6s\u2013R\u00e9nyi laws for dynamical systems","publication_year":2012,"publication_date":"2012-11-27","ids":{"openalex":"https://openalex.org/W2165735494","doi":"https://doi.org/10.1112/jlms/jds060","mag":"2165735494"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jds060","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jds060","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086002611","display_name":"Manfred Denker","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Manfred Denker","raw_affiliation_strings":["Department of Mathematics, Pennsylvania State University, State College, PA 16802, USA,","Department of Mathematics, Pennsylvania State University, State College, PA 16802, USA, [email protected]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pennsylvania State University, State College, PA 16802, USA,","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Mathematics, Pennsylvania State University, State College, PA 16802, USA, [email protected]","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057203573","display_name":"Matthew Nicol","orcid":"https://orcid.org/0000-0002-9217-5291"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew Nicol","raw_affiliation_strings":["Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA","institution_ids":["https://openalex.org/I44461941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057203573"],"corresponding_institution_ids":["https://openalex.org/I44461941"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.4192,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.62067773,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"87","issue":"2","first_page":"497","last_page":"508"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9997000098228455,"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":0.9997000098228455,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9611999988555908,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9564999938011169,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7471016645431519},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.6977629661560059},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6235855221748352},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.561016321182251},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5356317162513733},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.4968104660511017},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4804815351963043},{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"Law of large numbers","score":0.46648338437080383},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.46010056138038635},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.4378345310688019},{"id":"https://openalex.org/keywords/logistic-map","display_name":"Logistic map","score":0.43450605869293213},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.433510422706604},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41816246509552},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38363996148109436},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38189423084259033},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3229731321334839},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3076232373714447},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1270049810409546},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12455117702484131},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07360661029815674}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7471016645431519},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.6977629661560059},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6235855221748352},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.561016321182251},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5356317162513733},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.4968104660511017},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4804815351963043},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.46648338437080383},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.46010056138038635},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.4378345310688019},{"id":"https://openalex.org/C205330730","wikidata":"https://www.wikidata.org/wiki/Q587182","display_name":"Logistic map","level":3,"score":0.43450605869293213},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.433510422706604},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41816246509552},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38363996148109436},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38189423084259033},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3229731321334839},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3076232373714447},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1270049810409546},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12455117702484131},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07360661029815674},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1112/jlms/jds060","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jds060","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.706.486","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.706.486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uh.edu/%7Enicol/pdffiles/denker_latest2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6399999856948853}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1488877410","https://openalex.org/W1973494188","https://openalex.org/W1990068054","https://openalex.org/W2001390538","https://openalex.org/W2011216731","https://openalex.org/W2020169952","https://openalex.org/W2021254505","https://openalex.org/W2025551626","https://openalex.org/W2040404867","https://openalex.org/W2051111052","https://openalex.org/W2053013517","https://openalex.org/W2066127509","https://openalex.org/W2072996193","https://openalex.org/W2074335903","https://openalex.org/W2090887848","https://openalex.org/W2154767314","https://openalex.org/W3007989391"],"related_works":["https://openalex.org/W2083912123","https://openalex.org/W1995753472","https://openalex.org/W2007498995","https://openalex.org/W2070363207","https://openalex.org/W2387235960","https://openalex.org/W2936454922","https://openalex.org/W2063829812","https://openalex.org/W2385963768","https://openalex.org/W2082152426","https://openalex.org/W2963889409"],"abstract_inverted_index":{"We":[0,37,62],"establish":[1,78],"Erd\u00f6s\u2013R\u00e9nyi":[2],"limit":[3,20,70],"laws":[4,21],"for":[5,72,83],"Lipschitz":[6],"observations":[7,51],"on":[8,41,52],"a":[9,27,31,45,56,79],"class":[10],"of":[11,26,34,44,59,66,74],"non-uniformly":[12],"expanding":[13],"dynamical":[14],"systems,":[15],"including":[16],"logistic-like":[17],"maps.":[18,85],"These":[19],"give":[22,39],"the":[23,64,69],"maximal":[24,42],"average":[25],"time":[28,32,46,57],"series":[29,47],"over":[30,55],"window":[33,58],"logarithmic":[35],"length.":[36,61],"also":[38],"results":[40],"averages":[43],"arising":[48],"from":[49],"H\u00f6lder":[50],"intermittent-type":[53],"maps":[54],"polynomial":[60],"consider":[63],"rate":[65,81],"convergence":[67],"in":[68],"law":[71],"subshifts":[73],"finite":[75],"type":[76],"and":[77],"one-sided":[80],"bound":[82],"Gibbs\u2013Markov":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}