{"id":"https://openalex.org/W1990731756","doi":"https://doi.org/10.1142/s021812740802210x","title":"RELATIVE KOLMOGOROV ENTROPY OF A CHAOTIC SYSTEM IN THE PRESENCE OF NOISE","display_name":"RELATIVE KOLMOGOROV ENTROPY OF A CHAOTIC SYSTEM IN THE PRESENCE OF NOISE","publication_year":2008,"publication_date":"2008-09-01","ids":{"openalex":"https://openalex.org/W1990731756","doi":"https://doi.org/10.1142/s021812740802210x","mag":"1990731756"},"language":"en","primary_location":{"id":"doi:10.1142/s021812740802210x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740802210x","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/A5024730767","display_name":"\u0412. \u0421. \u0410\u043d\u0438\u0449\u0435\u043d\u043a\u043e","orcid":"https://orcid.org/0000-0003-2255-1498"},"institutions":[{"id":"https://openalex.org/I125219893","display_name":"Saratov State University","ror":"https://ror.org/05jcsqx24","country_code":"RU","type":"education","lineage":["https://openalex.org/I125219893"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"VADIM S. ANISHCHENKO","raw_affiliation_strings":["Saratov State University, 83, Astrakhanskaya Street, Saratov 410026, Russia","Saratov State University, 83 Astrakhanskaya Street, Saratov, 410026, Russia"],"affiliations":[{"raw_affiliation_string":"Saratov State University, 83, Astrakhanskaya Street, Saratov 410026, Russia","institution_ids":["https://openalex.org/I125219893"]},{"raw_affiliation_string":"Saratov State University, 83 Astrakhanskaya Street, Saratov, 410026, Russia","institution_ids":["https://openalex.org/I125219893"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032635474","display_name":"Sergey Astakhov","orcid":"https://orcid.org/0000-0002-7682-1919"},"institutions":[{"id":"https://openalex.org/I125219893","display_name":"Saratov State University","ror":"https://ror.org/05jcsqx24","country_code":"RU","type":"education","lineage":["https://openalex.org/I125219893"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"SERGEY ASTAKHOV","raw_affiliation_strings":["Saratov State University, 83, Astrakhanskaya Street, Saratov 410026, Russia","Saratov State University, 83 Astrakhanskaya Street, Saratov, 410026, Russia"],"affiliations":[{"raw_affiliation_string":"Saratov State University, 83, Astrakhanskaya Street, Saratov 410026, Russia","institution_ids":["https://openalex.org/I125219893"]},{"raw_affiliation_string":"Saratov State University, 83 Astrakhanskaya Street, Saratov, 410026, Russia","institution_ids":["https://openalex.org/I125219893"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024730767"],"corresponding_institution_ids":["https://openalex.org/I125219893"],"apc_list":null,"apc_paid":null,"fwci":0.2808,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.57216012,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","issue":"09","first_page":"2851","last_page":"2855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9842000007629395,"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/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.6994017958641052},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6898629069328308},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.5643690824508667},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5604098439216614},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5361535549163818},{"id":"https://openalex.org/keywords/generalized-relative-entropy","display_name":"Generalized relative entropy","score":0.5210889577865601},{"id":"https://openalex.org/keywords/quantum-relative-entropy","display_name":"Quantum relative entropy","score":0.5155046582221985},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5100389122962952},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.45683878660202026},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.4564705789089203},{"id":"https://openalex.org/keywords/entropy-estimation","display_name":"Entropy estimation","score":0.44318264722824097},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.4428562521934509},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.44274473190307617},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.23558703064918518},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1553959846496582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14310652017593384},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12502256035804749},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08602362871170044},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.06988105177879333},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.059542834758758545},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.055826276540756226}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6994017958641052},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6898629069328308},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.5643690824508667},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5604098439216614},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5361535549163818},{"id":"https://openalex.org/C5084201","wikidata":"https://www.wikidata.org/wiki/Q17090689","display_name":"Generalized relative entropy","level":5,"score":0.5210889577865601},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.5155046582221985},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5100389122962952},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.45683878660202026},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.4564705789089203},{"id":"https://openalex.org/C95546049","wikidata":"https://www.wikidata.org/wiki/Q1345207","display_name":"Entropy estimation","level":3,"score":0.44318264722824097},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.4428562521934509},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.44274473190307617},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.23558703064918518},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1553959846496582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14310652017593384},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12502256035804749},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08602362871170044},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.06988105177879333},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.059542834758758545},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.055826276540756226},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812740802210x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740802210x","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W613224089","https://openalex.org/W1802196594","https://openalex.org/W1967008192","https://openalex.org/W1979314372","https://openalex.org/W1995875735","https://openalex.org/W2000983461","https://openalex.org/W2031744814","https://openalex.org/W2056651346","https://openalex.org/W2079448718","https://openalex.org/W2081681829","https://openalex.org/W4292366057"],"related_works":["https://openalex.org/W1980795850","https://openalex.org/W1994292739","https://openalex.org/W2092814302","https://openalex.org/W2242607083","https://openalex.org/W4287111138","https://openalex.org/W1966497309","https://openalex.org/W3041843885","https://openalex.org/W2766006549","https://openalex.org/W2041435955","https://openalex.org/W3111928908"],"abstract_inverted_index":{"The":[0,17,35,77],"mixing":[1,45],"property":[2],"is":[3,10,20,33,58],"characterized":[4],"by":[5,12,86],"the":[6,42,54,63,82,87],"metric":[7,31,37,56,64],"entropy":[8,19,32,38,57,65,83],"that":[9],"introduced":[11],"Kolmogorov":[13,18],"for":[14,22,52,69],"dynamical":[15,48],"systems.":[16,49],"infinite":[21],"a":[23,29],"stochastic":[24],"system.":[25],"In":[26],"this":[27],"work,":[28],"relative":[30,36,55],"considered.":[34],"allows":[39],"to":[40,81],"estimate":[41],"level":[43],"of":[44,62],"in":[46],"noisy":[47],"An":[50],"algorithm":[51],"calculating":[53],"described":[59],"and":[60],"examples":[61],"estimation":[66,84],"are":[67,79],"provided":[68],"certain":[70],"chaotic":[71],"systems":[72],"with":[73],"various":[74],"noise":[75],"intensities.":[76],"results":[78],"compared":[80],"given":[85],"positive":[88],"Lyapunov":[89],"exponents.":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
