{"id":"https://openalex.org/W4386525526","doi":"https://doi.org/10.3390/axioms12090860","title":"Finite Chaoticity and Pairwise Sensitivity of a Strong-Mixing Measure-Preserving Semi-Flow","display_name":"Finite Chaoticity and Pairwise Sensitivity of a Strong-Mixing Measure-Preserving Semi-Flow","publication_year":2023,"publication_date":"2023-09-07","ids":{"openalex":"https://openalex.org/W4386525526","doi":"https://doi.org/10.3390/axioms12090860"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12090860","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090860","pdf_url":"https://www.mdpi.com/2075-1680/12/9/860/pdf?version=1694066696","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/9/860/pdf?version=1694066696","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010524764","display_name":"Risong Li","orcid":"https://orcid.org/0000-0003-3381-5786"},"institutions":[{"id":"https://openalex.org/I79223203","display_name":"Guangdong Ocean University","ror":"https://ror.org/0462wa640","country_code":"CN","type":"education","lineage":["https://openalex.org/I79223203"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Risong Li","raw_affiliation_strings":["School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China","institution_ids":["https://openalex.org/I79223203"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050079981","display_name":"Jingmin Pi","orcid":null},"institutions":[{"id":"https://openalex.org/I64852412","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23","country_code":"CN","type":"education","lineage":["https://openalex.org/I64852412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingmin Pi","raw_affiliation_strings":["College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China","institution_ids":["https://openalex.org/I64852412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101752493","display_name":"Yongjiang Li","orcid":"https://orcid.org/0000-0001-9247-573X"},"institutions":[{"id":"https://openalex.org/I79223203","display_name":"Guangdong Ocean University","ror":"https://ror.org/0462wa640","country_code":"CN","type":"education","lineage":["https://openalex.org/I79223203"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongjiang Li","raw_affiliation_strings":["School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China","institution_ids":["https://openalex.org/I79223203"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074030748","display_name":"Tianxiu Lu","orcid":"https://orcid.org/0000-0002-8806-9656"},"institutions":[{"id":"https://openalex.org/I64852412","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23","country_code":"CN","type":"education","lineage":["https://openalex.org/I64852412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tianxiu Lu","raw_affiliation_strings":["College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China","institution_ids":["https://openalex.org/I64852412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100410426","display_name":"Jianjun Wang","orcid":"https://orcid.org/0000-0002-5344-4460"},"institutions":[{"id":"https://openalex.org/I37574244","display_name":"Sichuan Agricultural University","ror":"https://ror.org/0388c3403","country_code":"CN","type":"education","lineage":["https://openalex.org/I37574244"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianjun Wang","raw_affiliation_strings":["Department of Mathematics, Sichuan Agricultural University, Yaan 625014, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan Agricultural University, Yaan 625014, China","institution_ids":["https://openalex.org/I37574244"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014911827","display_name":"Xianfeng Ding","orcid":"https://orcid.org/0000-0002-0275-1292"},"institutions":[{"id":"https://openalex.org/I165745306","display_name":"Southwest Petroleum University","ror":"https://ror.org/03h17x602","country_code":"CN","type":"education","lineage":["https://openalex.org/I165745306"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianfeng Ding","raw_affiliation_strings":["School of Science, Southwest Petroleum University, Chengdu 610500, China"],"affiliations":[{"raw_affiliation_string":"School of Science, Southwest Petroleum University, Chengdu 610500, China","institution_ids":["https://openalex.org/I165745306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5074030748","https://openalex.org/A5101752493"],"corresponding_institution_ids":["https://openalex.org/I64852412","https://openalex.org/I79223203"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20513604,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"9","first_page":"860","last_page":"860"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.998199999332428,"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":0.998199999332428,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9922999739646912,"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/pairwise-comparison","display_name":"Pairwise comparison","score":0.7119005918502808},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.7060859203338623},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6484630703926086},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.6360917687416077},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6060864329338074},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5817621350288391},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5125579833984375},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5043100118637085},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.49936747550964355},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4718185365200043},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.44903892278671265},{"id":"https://openalex.org/keywords/information-flow","display_name":"Information flow","score":0.4295912981033325},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38186025619506836},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23964011669158936},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.23557725548744202},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.15385732054710388},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1493121087551117},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08950921893119812},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08365848660469055}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7119005918502808},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.7060859203338623},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6484630703926086},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.6360917687416077},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6060864329338074},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5817621350288391},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5125579833984375},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5043100118637085},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.49936747550964355},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4718185365200043},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44903892278671265},{"id":"https://openalex.org/C2779136372","wikidata":"https://www.wikidata.org/wiki/Q10283002","display_name":"Information flow","level":2,"score":0.4295912981033325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38186025619506836},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23964011669158936},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.23557725548744202},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.15385732054710388},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1493121087551117},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08950921893119812},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08365848660469055},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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":3,"locations":[{"id":"doi:10.3390/axioms12090860","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090860","pdf_url":"https://www.mdpi.com/2075-1680/12/9/860/pdf?version=1694066696","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6be688a2fe874a7787170e037753d2b2","is_oa":true,"landing_page_url":"https://doaj.org/article/6be688a2fe874a7787170e037753d2b2","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 9, p 860 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/9/860/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12090860","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12090860","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090860","pdf_url":"https://www.mdpi.com/2075-1680/12/9/860/pdf?version=1694066696","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2516135519","display_name":null,"funder_award_id":"2023NSFSC007","funder_id":"https://openalex.org/F4320329861","funder_display_name":"Natural Science Foundation of Sichuan Province"},{"id":"https://openalex.org/G347856190","display_name":null,"funder_award_id":"2023NSFSC0070","funder_id":"https://openalex.org/F4320329861","funder_display_name":"Natural Science Foundation of Sichuan Province"},{"id":"https://openalex.org/G5639015145","display_name":null,"funder_award_id":"2022NSFSC1821","funder_id":"https://openalex.org/F4320329861","funder_display_name":"Natural Science Foundation of Sichuan Province"},{"id":"https://openalex.org/G681167465","display_name":null,"funder_award_id":"2020RC24","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"},{"id":"https://openalex.org/G7216457744","display_name":null,"funder_award_id":"2022NSFSC","funder_id":"https://openalex.org/F4320329861","funder_display_name":"Natural Science Foundation of Sichuan Province"},{"id":"https://openalex.org/G7836444726","display_name":null,"funder_award_id":"2020QT13","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"}],"funders":[{"id":"https://openalex.org/F4320322947","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23"},{"id":"https://openalex.org/F4320329861","display_name":"Natural Science Foundation of Sichuan Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386525526.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1963796392","https://openalex.org/W1966383052","https://openalex.org/W1980530496","https://openalex.org/W1985194270","https://openalex.org/W1989722359","https://openalex.org/W2001162474","https://openalex.org/W2003541147","https://openalex.org/W2022974863","https://openalex.org/W2036715020","https://openalex.org/W2040161418","https://openalex.org/W2047840488","https://openalex.org/W2049466345","https://openalex.org/W2083888232","https://openalex.org/W2084525984","https://openalex.org/W2090291554","https://openalex.org/W2091896339","https://openalex.org/W2255744044","https://openalex.org/W2378315582","https://openalex.org/W2402809068","https://openalex.org/W2548262653","https://openalex.org/W2586807479","https://openalex.org/W2891656133","https://openalex.org/W2912697496","https://openalex.org/W2923054028","https://openalex.org/W2964290034","https://openalex.org/W3038005217","https://openalex.org/W3095129776","https://openalex.org/W3099290845","https://openalex.org/W3112638805","https://openalex.org/W3164491485","https://openalex.org/W3178269943","https://openalex.org/W3193438539","https://openalex.org/W4223516921","https://openalex.org/W4230278731","https://openalex.org/W4231009334","https://openalex.org/W4239398473","https://openalex.org/W4249901819","https://openalex.org/W4256081943","https://openalex.org/W6646681443","https://openalex.org/W6787097396","https://openalex.org/W6989893776"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2942366970","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2562400057","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W4360593462","https://openalex.org/W2194570607"],"abstract_inverted_index":{"Chaos":[0],"is":[1,11],"a":[2],"common":[3],"phenomenon":[4],"in":[5,39,96,114],"nature":[6],"and":[7,18,23,46,66,72,91,94,102],"social":[8],"sciences.":[9],"As":[10],"well":[12],"known,":[13],"chaos":[14],"has":[15],"multiple":[16],"definitions,":[17],"there":[19],"are":[20],"both":[21,77],"differences":[22],"connections":[24],"between":[25],"them.":[26],"The":[27],"unique":[28],"properties":[29],"of":[30,111],"chaotic":[31,65],"systems":[32,117],"can":[33],"be":[34],"leveraged":[35],"to":[36,60,118],"address":[37],"challenges":[38],"communication,":[40],"security,":[41,98],"data":[42],"processing,":[43],"system":[44],"analysis,":[45],"control":[47],"across":[48],"different":[49],"domains.":[50],"For":[51],"semi-flows,":[52],"this":[53],"paper":[54,106],"introduces":[55],"two":[56,80,84],"important":[57,92],"concepts":[58,85],"corresponding":[59,112],"discrete":[61,115],"dynamical":[62,116],"systems,":[63],"finitely":[64],"pairwise":[67],"sensitivity.":[68],"Since":[69],"Tent":[70],"map":[71],"its":[73],"induced":[74],"suspended":[75],"semi-flows":[76,88],"have":[78,89],"these":[79,83],"properties,":[81],"then":[82],"on":[86],"the":[87,108],"extensive":[90],"applications":[93],"meanings":[95],"information":[97],"finance,":[99],"artificial":[100],"intelligence":[101],"other":[103],"fields.":[104],"This":[105],"extends":[107],"vast":[109],"majority":[110],"results":[113],"semi-flows.":[119]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
