{"id":"https://openalex.org/W4414459946","doi":"https://doi.org/10.1007/s00498-025-00423-x","title":"The distributional Koopman operator for random dynamical systems","display_name":"The distributional Koopman operator for random dynamical systems","publication_year":2025,"publication_date":"2025-09-24","ids":{"openalex":"https://openalex.org/W4414459946","doi":"https://doi.org/10.1007/s00498-025-00423-x"},"language":"en","primary_location":{"id":"doi:10.1007/s00498-025-00423-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00498-025-00423-x","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","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/A5003545965","display_name":"Maria Oprea","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maria Oprea","raw_affiliation_strings":["Center for Applied Mathematics, Cornell University, Ithaca, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics, Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003110773","display_name":"Alex Townsend","orcid":"https://orcid.org/0000-0002-8183-7077"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alex Townsend","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003942837","display_name":"Yunan Yang","orcid":"https://orcid.org/0000-0001-7238-7978"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yunan Yang","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003110773"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1780137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"4","first_page":"769","last_page":"798"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transfer-operator","display_name":"Transfer operator","score":0.7605999708175659},{"id":"https://openalex.org/keywords/dynamic-mode-decomposition","display_name":"Dynamic mode decomposition","score":0.7282999753952026},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6287000179290771},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6175000071525574},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.597599983215332},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5282999873161316},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.5109000205993652},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.46000000834465027},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4593999981880188}],"concepts":[{"id":"https://openalex.org/C2777952282","wikidata":"https://www.wikidata.org/wiki/Q3354606","display_name":"Transfer operator","level":2,"score":0.7605999708175659},{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.7282999753952026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7159000039100647},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6287000179290771},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6175000071525574},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.597599983215332},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5282999873161316},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.5109000205993652},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46299999952316284},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.46000000834465027},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4593999981880188},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.44020000100135803},{"id":"https://openalex.org/C193817511","wikidata":"https://www.wikidata.org/wiki/Q7291964","display_name":"Random dynamical system","level":4,"score":0.4088999927043915},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.39899998903274536},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.34389999508857727},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3310999870300293},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.3255999982357025},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C135694725","wikidata":"https://www.wikidata.org/wiki/Q1201087","display_name":"Detailed balance","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.25600001215934753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00498-025-00423-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00498-025-00423-x","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4206087872","display_name":null,"funder_award_id":"DMS-2045646","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6204413252","display_name":null,"funder_award_id":"N00014-23-1-2729","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7069032464","display_name":null,"funder_award_id":"DMS-2409855","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G948203765","display_name":null,"funder_award_id":"N00014-24-1-2088","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W234899517","https://openalex.org/W1585160083","https://openalex.org/W1591018827","https://openalex.org/W1997054581","https://openalex.org/W2051542100","https://openalex.org/W2164954534","https://openalex.org/W2615735362","https://openalex.org/W2730644873","https://openalex.org/W2795067111","https://openalex.org/W2802739963","https://openalex.org/W2973022759","https://openalex.org/W3010758268","https://openalex.org/W3035145762","https://openalex.org/W3038118776","https://openalex.org/W3094983888","https://openalex.org/W3098781239","https://openalex.org/W3101392902","https://openalex.org/W3123743774","https://openalex.org/W3126331428","https://openalex.org/W3216122675","https://openalex.org/W4214724636","https://openalex.org/W4248931215","https://openalex.org/W4300093168","https://openalex.org/W4312258136","https://openalex.org/W4390144100","https://openalex.org/W4399464012"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}