{"id":"https://openalex.org/W3022816144","doi":"https://doi.org/10.1137/20m1336576","title":"Conley's Fundamental Theorem for a Class of Hybrid Systems","display_name":"Conley's Fundamental Theorem for a Class of Hybrid Systems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3022816144","doi":"https://doi.org/10.1137/20m1336576","mag":"3022816144"},"language":"en","primary_location":{"id":"doi:10.1137/20m1336576","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1336576","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2005.03217","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068996884","display_name":"Matthew D. Kvalheim","orcid":"https://orcid.org/0000-0002-2662-6760"},"institutions":[{"id":"https://openalex.org/I36788626","display_name":"California University of Pennsylvania","ror":"https://ror.org/01spssf70","country_code":"US","type":"education","lineage":["https://openalex.org/I36788626"]},{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew D. Kvalheim","raw_affiliation_strings":["#N#               * University of Pennsylvania"],"raw_orcid":"https://orcid.org/0000-0002-2662-6760","affiliations":[{"raw_affiliation_string":"#N#               * University of Pennsylvania","institution_ids":["https://openalex.org/I36788626","https://openalex.org/I79576946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002498364","display_name":"Paul Gustafson","orcid":"https://orcid.org/0000-0001-8200-1725"},"institutions":[{"id":"https://openalex.org/I19648265","display_name":"Wright State University","ror":"https://ror.org/04qk6pt94","country_code":"US","type":"education","lineage":["https://openalex.org/I19648265"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Gustafson","raw_affiliation_strings":["Wright State University;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wright State University;","institution_ids":["https://openalex.org/I19648265"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082032878","display_name":"Daniel E. Koditschek","orcid":"https://orcid.org/0000-0001-5188-1352"},"institutions":[{"id":"https://openalex.org/I36788626","display_name":"California University of Pennsylvania","ror":"https://ror.org/01spssf70","country_code":"US","type":"education","lineage":["https://openalex.org/I36788626"]},{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel E. Koditschek","raw_affiliation_strings":["#N#               * University of Pennsylvania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N#               * University of Pennsylvania","institution_ids":["https://openalex.org/I36788626","https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0726,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.29626306,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"20","issue":"2","first_page":"784","last_page":"825"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.729975700378418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6859981417655945},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6238644123077393},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5426469445228577},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5091235041618347},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.4985325336456299},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.48908406496047974},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4570072591304779},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4515482783317566},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43518829345703125},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.38790497183799744},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3573690950870514},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21440759301185608},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14644619822502136},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.13437792658805847},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13135406374931335},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1293487548828125},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.1208164393901825}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.729975700378418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6859981417655945},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6238644123077393},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5426469445228577},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5091235041618347},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.4985325336456299},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.48908406496047974},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4570072591304779},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4515482783317566},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43518829345703125},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.38790497183799744},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3573690950870514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21440759301185608},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14644619822502136},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.13437792658805847},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13135406374931335},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1293487548828125},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.1208164393901825},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/20m1336576","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1336576","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2005.03217","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.03217","pdf_url":"https://arxiv.org/pdf/2005.03217","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:mdsoar.org:11603/30364","is_oa":true,"landing_page_url":"http://hdl.handle.net/11603/30364","pdf_url":"https://mdsoar.org/bitstreams/c386ad5c-a2d4-48c2-81a5-b4d277a8c7ea/download","source":{"id":"https://openalex.org/S4306402556","display_name":"Maryland Shared Open Access Repository (USMAI Consortium)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"mag:3022816144","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2005.03217","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2005.03217","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2005.03217","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.13016/m2zlha-lark","is_oa":true,"landing_page_url":"https://doi.org/10.13016/m2zlha-lark","pdf_url":null,"source":{"id":"https://openalex.org/S4306402644","display_name":"Digital Repository at the University of Maryland (University of Maryland College Park)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66946132","host_organization_name":"University of Maryland, College Park","host_organization_lineage":["https://openalex.org/I66946132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2005.03217","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.03217","pdf_url":"https://arxiv.org/pdf/2005.03217","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1740622364","display_name":null,"funder_award_id":"N00014-16-1-2817","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G3685741416","display_name":null,"funder_award_id":"W911NF1810327","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G5877274225","display_name":null,"funder_award_id":"N00014-16-1-2817","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G739330327","display_name":null,"funder_award_id":"W911-NF-1810327","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8651847824","display_name":null,"funder_award_id":"10601110D8Z","funder_id":"https://openalex.org/F4320333578","funder_display_name":"Office of the Under Secretary of Defense"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320333578","display_name":"Office of the Under Secretary of Defense","ror":null},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":79,"referenced_works":["https://openalex.org/W162901799","https://openalex.org/W584990872","https://openalex.org/W1500850050","https://openalex.org/W1514218977","https://openalex.org/W1515237213","https://openalex.org/W1520671517","https://openalex.org/W1524590822","https://openalex.org/W1543608798","https://openalex.org/W1544390368","https://openalex.org/W1550227333","https://openalex.org/W1550247484","https://openalex.org/W1572164227","https://openalex.org/W1573152848","https://openalex.org/W1592335142","https://openalex.org/W1736530648","https://openalex.org/W1881337225","https://openalex.org/W1887343820","https://openalex.org/W1971035315","https://openalex.org/W1974198739","https://openalex.org/W1977134231","https://openalex.org/W1981287404","https://openalex.org/W1983815930","https://openalex.org/W1983918081","https://openalex.org/W1985660326","https://openalex.org/W2013284908","https://openalex.org/W2017493230","https://openalex.org/W2019261882","https://openalex.org/W2024574047","https://openalex.org/W2027005420","https://openalex.org/W2027703680","https://openalex.org/W2028617788","https://openalex.org/W2029359030","https://openalex.org/W2032214729","https://openalex.org/W2041103407","https://openalex.org/W2052683749","https://openalex.org/W2066967910","https://openalex.org/W2068864491","https://openalex.org/W2072149862","https://openalex.org/W2074592759","https://openalex.org/W2080819368","https://openalex.org/W2081295695","https://openalex.org/W2089344586","https://openalex.org/W2091316349","https://openalex.org/W2097894461","https://openalex.org/W2099308299","https://openalex.org/W2102892532","https://openalex.org/W2107746850","https://openalex.org/W2111328528","https://openalex.org/W2117218135","https://openalex.org/W2120548794","https://openalex.org/W2121829700","https://openalex.org/W2121922603","https://openalex.org/W2128131727","https://openalex.org/W2129231075","https://openalex.org/W2129966419","https://openalex.org/W2134260093","https://openalex.org/W2137547873","https://openalex.org/W2140943160","https://openalex.org/W2146139464","https://openalex.org/W2146227737","https://openalex.org/W2172178670","https://openalex.org/W2203377825","https://openalex.org/W2461166651","https://openalex.org/W2496648954","https://openalex.org/W2566720177","https://openalex.org/W2793122067","https://openalex.org/W2901264773","https://openalex.org/W2962988082","https://openalex.org/W2964071034","https://openalex.org/W2970660754","https://openalex.org/W2974596055","https://openalex.org/W2991400276","https://openalex.org/W2999060662","https://openalex.org/W3040586665","https://openalex.org/W3120971098","https://openalex.org/W4212928962","https://openalex.org/W4232372160","https://openalex.org/W4245639461","https://openalex.org/W4249981769"],"related_works":["https://openalex.org/W2896542238","https://openalex.org/W3165596857","https://openalex.org/W2055327456","https://openalex.org/W2738361875","https://openalex.org/W2086547311","https://openalex.org/W3125489066","https://openalex.org/W2337959856","https://openalex.org/W3124122650","https://openalex.org/W345085093","https://openalex.org/W2552102967","https://openalex.org/W1592357181","https://openalex.org/W2089362396","https://openalex.org/W1761765533","https://openalex.org/W2751472019","https://openalex.org/W2047878675","https://openalex.org/W3041497075","https://openalex.org/W3020818407","https://openalex.org/W2015070325","https://openalex.org/W2411664774"],"abstract_inverted_index":{"We":[0],"establish":[1],"versions":[2],"of":[3,16,23,67,85,108,120,138],"Conley's":[4,143],"(i)":[5,24],"fundamental":[6],"theorem":[7,11],"and":[8,44,87,91,126],"(ii)":[9],"decomposition":[10],"for":[12,34,89],"a":[13,27,56,64],"broad":[14],"class":[15,66],"hybrid":[17,21,36,69,129],"dynamical":[18,93],"systems.":[19],"The":[20],"version":[22],"asserts":[25],"that":[26,141],"globally-defined":[28],"\"hybrid":[29],"complete":[30],"Lyapunov":[31],"function\"":[32],"exists":[33],"every":[35],"system":[37],"in":[38,55,75,116,147],"this":[39],"class.":[40],"Motivated":[41],"by":[42],"mechanics":[43],"control":[45],"settings":[46],"where":[47],"physical":[48],"or":[49],"engineered":[50],"events":[51],"cause":[52],"abrupt":[53],"changes":[54],"system's":[57],"governing":[58],"dynamics,":[59],"our":[60,106],"results":[61,82],"apply":[62],"to":[63],"large":[65],"Lagrangian":[68],"systems":[70,130],"(with":[71],"impacts)":[72],"studied":[73],"extensively":[74],"the":[76,117,133],"robotics":[77],"literature.":[78],"Viewed":[79],"formally,":[80],"these":[81],"generalize":[83],"those":[84,148],"Conley":[86],"Franks":[88],"continuous-time":[90],"discrete-time":[92],"systems,":[94],"respectively,":[95],"on":[96],"metric":[97],"spaces.":[98],"However,":[99],"we":[100],"furnish":[101],"specific":[102],"examples":[103],"illustrating":[104],"how":[105],"statement":[107],"sufficient":[109],"conditions":[110],"represents":[111],"merely":[112],"an":[113],"early":[114],"step":[115],"longer":[118],"project":[119],"establishing":[121],"what":[122],"formal":[123],"assumptions":[124],"can":[125],"cannot":[127],"endow":[128],"models":[131],"with":[132],"topologically":[134],"well":[135],"characterized":[136],"partitions":[137],"limit":[139],"behavior":[140],"make":[142],"theory":[144],"so":[145],"valuable":[146],"classical":[149],"settings.":[150]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}