{"id":"https://openalex.org/W2014837736","doi":"https://doi.org/10.1142/s0218127408020203","title":"DENSITY OF MEASURE-THEORETIC DIRECTIONAL ENTROPY FOR LATTICE DYNAMICAL SYSTEMS","display_name":"DENSITY OF MEASURE-THEORETIC DIRECTIONAL ENTROPY FOR LATTICE DYNAMICAL SYSTEMS","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2014837736","doi":"https://doi.org/10.1142/s0218127408020203","mag":"2014837736"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127408020203","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408020203","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5013556333","display_name":"M. Courbage","orcid":"https://orcid.org/0000-0001-6615-9039"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210127056","display_name":"Laboratoire Mati\u00e8re et Syst\u00e8mes Complexes","ror":"https://ror.org/032w6q449","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210095849","https://openalex.org/I4210127056"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"M. COURBAGE","raw_affiliation_strings":["Laboratoire Mati\u00e8re et Syst\u00e8mes Complexes (MSC), UMR 7057 CNRS et Universit\u00e9 Paris 7-Denis Diderot, Case 7020, Tour 24-14, 5\u00e8me \u00e9tage, 75251 Paris Cedex 05, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Mati\u00e8re et Syst\u00e8mes Complexes (MSC), UMR 7057 CNRS et Universit\u00e9 Paris 7-Denis Diderot, Case 7020, Tour 24-14, 5\u00e8me \u00e9tage, 75251 Paris Cedex 05, France","institution_ids":["https://openalex.org/I4210127056","https://openalex.org/I204730241","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045701524","display_name":"B. Kami\u0144ski","orcid":"https://orcid.org/0000-0003-4779-8729"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"B. KAMI\u0143SKI","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toru\u0144, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013556333"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210127056"],"apc_list":null,"apc_paid":null,"fwci":0.4368,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57659058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":"01","first_page":"161","last_page":"168"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9904000163078308,"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/T10244","display_name":"Chaos control and synchronization","score":0.9858999848365784,"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/mathematics","display_name":"Mathematics","score":0.6865714192390442},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5806423425674438},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5297155380249023},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5134187936782837},{"id":"https://openalex.org/keywords/measure-preserving-dynamical-system","display_name":"Measure-preserving dynamical system","score":0.4466007947921753},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.4419924020767212},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.42583537101745605},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.40817907452583313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3783770203590393},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26900574564933777},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.26495060324668884},{"id":"https://openalex.org/keywords/random-dynamical-system","display_name":"Random dynamical system","score":0.23635047674179077},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2314755916595459},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1738114058971405},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.12652409076690674},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07459220290184021}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6865714192390442},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5806423425674438},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5297155380249023},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5134187936782837},{"id":"https://openalex.org/C175197506","wikidata":"https://www.wikidata.org/wiki/Q1003225","display_name":"Measure-preserving dynamical system","level":5,"score":0.4466007947921753},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.4419924020767212},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.42583537101745605},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.40817907452583313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3783770203590393},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26900574564933777},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.26495060324668884},{"id":"https://openalex.org/C193817511","wikidata":"https://www.wikidata.org/wiki/Q7291964","display_name":"Random dynamical system","level":4,"score":0.23635047674179077},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2314755916595459},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1738114058971405},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.12652409076690674},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07459220290184021},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127408020203","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408020203","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W957133684","https://openalex.org/W1968599697","https://openalex.org/W1982622595","https://openalex.org/W2006216095","https://openalex.org/W2006952311","https://openalex.org/W2029261339","https://openalex.org/W2036713164","https://openalex.org/W2047743257","https://openalex.org/W2507047444","https://openalex.org/W4231009334","https://openalex.org/W6697443619"],"related_works":["https://openalex.org/W140420611","https://openalex.org/W2062595969","https://openalex.org/W1993383002","https://openalex.org/W2044696633","https://openalex.org/W593947393","https://openalex.org/W2122673857","https://openalex.org/W4388681848","https://openalex.org/W2053145346","https://openalex.org/W593885246","https://openalex.org/W397552692"],"abstract_inverted_index":{"The":[0],"density":[1,30],"of":[2,35],"the":[3,8,26,29,33,36,54,62],"measure-theoretic":[4],"directional":[5],"entropy":[6,34],"for":[7,19],"lattice":[9,21],"dynamical":[10,22],"system":[11],"is":[12,16,47,57],"introduced":[13],"and":[14],"it":[15,46],"shown":[17],"that":[18,60],"a":[20,48],"transformation":[23,28],"commuting":[24],"with":[25,32,51],"shift":[27],"coincides":[31],"\u2124":[37],"2":[38],"-action":[39],"generated":[40],"by":[41],"these":[42],"two":[43],"transformations,":[44],"i.e.":[45],"constant":[49],"function":[50],"respect":[52],"to":[53,68],"direction.":[55],"It":[56],"also":[58],"proved":[59],"in":[61],"noncommutative":[63],"case":[64],"this":[65],"result":[66],"fails":[67],"be":[69],"true.":[70]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}