{"id":"https://openalex.org/W2914323890","doi":"https://doi.org/10.1137/18m1197862","title":"Measure-Theoretic Invariance Entropy for Control Systems","display_name":"Measure-Theoretic Invariance Entropy for Control Systems","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2914323890","doi":"https://doi.org/10.1137/18m1197862","mag":"2914323890"},"language":"en","primary_location":{"id":"doi:10.1137/18m1197862","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1197862","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5101933922","display_name":"Tao Wang","orcid":"https://orcid.org/0000-0002-3844-7794"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tao Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100655967","display_name":"Yu Huang","orcid":"https://orcid.org/0009-0008-9608-0020"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu Huang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101501154","display_name":"Hai\u2010Wei Sun","orcid":"https://orcid.org/0000-0002-5507-6083"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hai-Wei Sun","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101933922"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7552,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.97019992,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"57","issue":"1","first_page":"310","last_page":"333"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9979000091552734,"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":0.9979000091552734,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9815000295639038,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8057788014411926},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.6375666856765747},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6211861371994019},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6190928220748901},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5062764883041382},{"id":"https://openalex.org/keywords/scale-invariance","display_name":"Scale invariance","score":0.4360795319080353},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4228171706199646},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.19431018829345703},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08843857049942017},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07911568880081177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07793024182319641},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05962479114532471}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8057788014411926},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.6375666856765747},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6211861371994019},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6190928220748901},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5062764883041382},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.4360795319080353},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4228171706199646},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.19431018829345703},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08843857049942017},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07911568880081177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07793024182319641},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05962479114532471},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1197862","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1197862","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4429429653","display_name":null,"funder_award_id":"11771459","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2011970734","https://openalex.org/W2095363739","https://openalex.org/W2096584475","https://openalex.org/W2157945087","https://openalex.org/W2160463528","https://openalex.org/W2324103067","https://openalex.org/W2534822964","https://openalex.org/W2784158305","https://openalex.org/W2962746801","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W4255837520","https://openalex.org/W2387011115","https://openalex.org/W4234808182","https://openalex.org/W4255628145","https://openalex.org/W2382043075","https://openalex.org/W2809151339","https://openalex.org/W2097033632","https://openalex.org/W2496965161","https://openalex.org/W2021670453","https://openalex.org/W2021783512"],"abstract_inverted_index":{"We":[0,30],"introduce":[1],"two":[2,46],"types":[3],"of":[4],"measure-theoretic":[5,39,52],"invariance":[6,34,40,53],"entropies":[7,18,35,54],"for":[8,28],"topological":[9,50],"time-invariant":[10],"control":[11],"systems.":[12],"It":[13],"is":[14],"shown":[15],"that":[16,33],"these":[17],"are":[19,36],"invariant":[20],"under":[21],"conjugacies":[22],"and":[23,51],"there":[24],"exists":[25],"a":[26],"generator":[27],"them.":[29],"also":[31],"illustrate":[32],"determined":[37],"by":[38],"entropies.":[41],"More":[42],"importantly,":[43],"we":[44],"establish":[45],"variational":[47],"principles":[48],"between":[49],"in":[55],"some":[56],"special":[57],"situations.":[58]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2026-03-01T08:55:55.761014","created_date":"2025-10-10T00:00:00"}