{"id":"https://openalex.org/W4200513569","doi":"https://doi.org/10.3390/sym13122326","title":"Turnpike Properties for Dynamical Systems Determined by Differential Inclusions","display_name":"Turnpike Properties for Dynamical Systems Determined by Differential Inclusions","publication_year":2021,"publication_date":"2021-12-04","ids":{"openalex":"https://openalex.org/W4200513569","doi":"https://doi.org/10.3390/sym13122326"},"language":"en","primary_location":{"id":"doi:10.3390/sym13122326","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122326","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2326/pdf?version=1638623679","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/12/2326/pdf?version=1638623679","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102814437","display_name":"Alexander J. Zaslavski","orcid":"https://orcid.org/0000-0002-6381-6459"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Alexander J. Zaslavski","raw_affiliation_strings":["Department of Mathematics, Technion\u2013Israel Institute of Technology, Haifa 32000, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technion\u2013Israel Institute of Technology, Haifa 32000, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102814437"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.2169,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50356141,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"13","issue":"12","first_page":"2326","last_page":"2326"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994999766349792,"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":0.9883000254631042,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/differential-inclusion","display_name":"Differential inclusion","score":0.9544458985328674},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.7679547071456909},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6727038621902466},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.6430206298828125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5242814421653748},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4948198199272156},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4773994982242584},{"id":"https://openalex.org/keywords/inclusion","display_name":"Inclusion (mineral)","score":0.41591739654541016},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36220812797546387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3478996753692627},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16530001163482666}],"concepts":[{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.9544458985328674},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.7679547071456909},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6727038621902466},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.6430206298828125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5242814421653748},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4948198199272156},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4773994982242584},{"id":"https://openalex.org/C109359841","wikidata":"https://www.wikidata.org/wiki/Q728944","display_name":"Inclusion (mineral)","level":2,"score":0.41591739654541016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36220812797546387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3478996753692627},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16530001163482666},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13122326","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122326","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2326/pdf?version=1638623679","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:dfedab065dd44418978ca22f5c6cf7da","is_oa":true,"landing_page_url":"https://doaj.org/article/dfedab065dd44418978ca22f5c6cf7da","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 12, p 2326 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/12/2326/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13122326","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13122326","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122326","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2326/pdf?version=1638623679","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7900000214576721,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4200513569.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W564300562","https://openalex.org/W637282818","https://openalex.org/W1489495359","https://openalex.org/W1986211050","https://openalex.org/W2024891059","https://openalex.org/W2050766281","https://openalex.org/W2060088282","https://openalex.org/W2069016790","https://openalex.org/W2073215497","https://openalex.org/W2079261393","https://openalex.org/W2257848148","https://openalex.org/W2469190861","https://openalex.org/W2479760086","https://openalex.org/W2489957437","https://openalex.org/W2587344637","https://openalex.org/W2594088463","https://openalex.org/W2613213659","https://openalex.org/W4210718478","https://openalex.org/W4232195521","https://openalex.org/W6720089610","https://openalex.org/W6722914953","https://openalex.org/W6732947208","https://openalex.org/W6734097140","https://openalex.org/W6738167505"],"related_works":["https://openalex.org/W2146846916","https://openalex.org/W2777927656","https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2330535098"],"abstract_inverted_index":{"In":[0,25],"this":[1,64],"paper,":[2],"we":[3,27,47,59,70],"study":[4],"the":[5,31,39,42,61],"turnpike":[6,40,62],"phenomenon":[7],"for":[8],"trajectories":[9,54,75],"of":[10,52,55,76],"continuous-time":[11],"dynamical":[12],"systems":[13],"generated":[14],"by":[15],"differential":[16,32],"inclusions,":[17],"which":[18],"have":[19],"a":[20,35,49],"prototype":[21],"in":[22],"mathematical":[23],"economics.":[24],"particular,":[26],"show":[28],"that,":[29],"if":[30,69],"inclusion":[33],"has":[34],"certain":[36],"symmetric":[37,44],"property,":[38],"possesses":[41],"corresponding":[43],"property.":[45],"If":[46],"know":[48,60],"finite":[50],"number":[51],"approximate":[53],"our":[56,77],"system,":[57],"then":[58],"and":[63],"information":[65],"can":[66],"be":[67],"useful":[68],"need":[71],"to":[72],"find":[73],"new":[74],"system":[78],"or":[79],"their":[80],"approximations.":[81]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}