{"id":"https://openalex.org/W2117892994","doi":"https://doi.org/10.1142/s0218127415500017","title":"The Hierarchy of Distributional Chaos","display_name":"The Hierarchy of Distributional Chaos","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2117892994","doi":"https://doi.org/10.1142/s0218127415500017","mag":"2117892994"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127415500017","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415500017","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/A5100616580","display_name":"Heman Fu","orcid":"https://orcid.org/0000-0002-1094-5046"},"institutions":[{"id":"https://openalex.org/I183816158","display_name":"Zhaoqing University","ror":"https://ror.org/025n5kj18","country_code":"CN","type":"education","lineage":["https://openalex.org/I183816158"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Heman Fu","raw_affiliation_strings":["School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, P. R. China","institution_ids":["https://openalex.org/I183816158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010018503","display_name":"Jincheng Xiong","orcid":null},"institutions":[{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jincheng Xiong","raw_affiliation_strings":["School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China","institution_ids":["https://openalex.org/I187400657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006177163","display_name":"Huoyun Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huoyun Wang","raw_affiliation_strings":["Department of Mathematics, Guangzhou University, Guangzhou 510006, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guangzhou University, Guangzhou 510006, P. R. China","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4998,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63625866,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"25","issue":"01","first_page":"1550001","last_page":"1550001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9890000224113464,"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":0.9890000224113464,"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/T10244","display_name":"Chaos control and synchronization","score":0.9218000173568726,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9023000001907349,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/chaos","display_name":"CHAOS (operating system)","score":0.718271017074585},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6301825046539307},{"id":"https://openalex.org/keywords/wedge","display_name":"Wedge (geometry)","score":0.6232861876487732},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.598756730556488},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5415937900543213},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4718320965766907},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4663941562175751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44741785526275635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4457658529281616},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.4310433864593506},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4262647032737732},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.4108760952949524},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.35644251108169556},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.1677422821521759},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15023434162139893},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14174625277519226},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1325153410434723},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10995590686798096},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.07164216041564941},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06668952107429504}],"concepts":[{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.718271017074585},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6301825046539307},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.6232861876487732},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.598756730556488},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5415937900543213},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4718320965766907},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4663941562175751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44741785526275635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4457658529281616},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4310433864593506},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4262647032737732},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.4108760952949524},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.35644251108169556},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.1677422821521759},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15023434162139893},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14174625277519226},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1325153410434723},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10995590686798096},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.07164216041564941},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06668952107429504},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127415500017","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415500017","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":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W608145207","https://openalex.org/W1970323476","https://openalex.org/W2008822020","https://openalex.org/W2026605936","https://openalex.org/W2095453288","https://openalex.org/W2097279366","https://openalex.org/W2148007321","https://openalex.org/W2477022665","https://openalex.org/W4239883234","https://openalex.org/W4242874622"],"related_works":["https://openalex.org/W2392447668","https://openalex.org/W2028445092","https://openalex.org/W2390824390","https://openalex.org/W1496745782","https://openalex.org/W2384000718","https://openalex.org/W2052017700","https://openalex.org/W4240432832","https://openalex.org/W3199731469","https://openalex.org/W2167530057","https://openalex.org/W2365276084"],"abstract_inverted_index":{"For":[0,19],"each":[1],"\u03bb":[2],"\u2208":[3,65],"[0,":[4,66],"1],":[5],"\u03bb-power":[6,52],"distributional":[7,17,74],"chaos":[8,75],"has":[9],"been":[10],"defined":[11],"via":[12],"Furstenberg":[13],"families":[14],"to":[15,82],"strengthen":[16],"chaos.":[18,90],"the":[20,87],"sake":[21],"of":[22,29,39,42,73,86,89],"distinguishing":[23],"them,":[24],"we":[25,45,69],"present":[26],"a":[27,36,71],"class":[28],"dynamical":[30,40],"systems,":[31],"called":[32],"wedge-shape":[33,48],"systems.":[34],"Through":[35],"thorough":[37],"analysis":[38],"behaviors":[41],"all":[43],"point-pairs,":[44],"show":[46],"that":[47],"systems":[49],"can":[50],"be":[51],"distributionally":[53,59],"chaotic":[54],"and":[55],"admit":[56],"no":[57],"\u03bb\u2032-power":[58],"scrambled":[60],"pairs":[61],"for":[62],"any":[63],"\u03bb\u2032":[64],"\u03bb).":[67],"Then":[68],"unfold":[70],"picture":[72],"with":[76],"rich":[77],"hierarchical":[78],"structures,":[79],"which":[80],"helps":[81],"improve":[83],"our":[84],"comprehension":[85],"diversity":[88]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
