{"id":"https://openalex.org/W2094361202","doi":"https://doi.org/10.1109/cdc.2009.5400512","title":"An approximate parametrization of the ergodic partition using time averaged observables","display_name":"An approximate parametrization of the ergodic partition using time averaged observables","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2094361202","doi":"https://doi.org/10.1109/cdc.2009.5400512","mag":"2094361202"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2009.5400512","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400512","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-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/A5004426104","display_name":"Marko Budi\u0161i\u0107","orcid":"https://orcid.org/0000-0002-4992-0284"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marko Budisic","raw_affiliation_strings":["Department of Mechanical Engineering, University of California,\uc2a0Santa Barbara, Santa Barbara, CA, USA","Department of Mechanical Engineering, University of California, Santa Barbara, 93106, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California,\uc2a0Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Santa Barbara, 93106, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014334832","display_name":"Igor Mezi\u0107","orcid":"https://orcid.org/0000-0002-2873-9013"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Igor Mezic","raw_affiliation_strings":["Department of Mechanical Engineering, University of California,\uc2a0Santa Barbara, Santa Barbara, CA, USA","Department of Mechanical Engineering, University of California, Santa Barbara, 93106, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California,\uc2a0Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Santa Barbara, 93106, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":0.7269,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.72716163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":null,"first_page":"3162","last_page":"3168"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9944999814033508,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9944999814033508,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9722999930381775,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9663000106811523,"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/ergodic-theory","display_name":"Ergodic theory","score":0.8997614979743958},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7065088748931885},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.5546219348907471},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5435391068458557},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.4943728446960449},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.48805081844329834},{"id":"https://openalex.org/keywords/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.4807136356830597},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.47760531306266785},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.45393574237823486},{"id":"https://openalex.org/keywords/diffusion-map","display_name":"Diffusion map","score":0.42503392696380615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32473376393318176},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.23242312669754028},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15837255120277405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1530059576034546},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09204527735710144},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06849515438079834}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.8997614979743958},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7065088748931885},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.5546219348907471},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5435391068458557},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4943728446960449},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.48805081844329834},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.4807136356830597},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.47760531306266785},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.45393574237823486},{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.42503392696380615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32473376393318176},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.23242312669754028},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15837255120277405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1530059576034546},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09204527735710144},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06849515438079834},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.0},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2009.5400512","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400512","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.941.8283","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.941.8283","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Marko_Budisic/publication/224109246_An_approximate_parametrization_of_the_ergodic_partition_using_time_averaged_observables/links/00b495329a4f05b831000000.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332500","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W112374705","https://openalex.org/W587265912","https://openalex.org/W1501770280","https://openalex.org/W1578099820","https://openalex.org/W1866611211","https://openalex.org/W1989368986","https://openalex.org/W1994330305","https://openalex.org/W2006554089","https://openalex.org/W2074388175","https://openalex.org/W2079746361","https://openalex.org/W2084430802","https://openalex.org/W2103890712","https://openalex.org/W2117684310","https://openalex.org/W2160163816","https://openalex.org/W2169243380","https://openalex.org/W2787852338","https://openalex.org/W3109381375","https://openalex.org/W4213367101","https://openalex.org/W4255338393"],"related_works":["https://openalex.org/W2134654202","https://openalex.org/W2057711290","https://openalex.org/W4298162610","https://openalex.org/W3048177030","https://openalex.org/W2950551861","https://openalex.org/W2026069322","https://openalex.org/W4300889323","https://openalex.org/W2070293309","https://openalex.org/W1971327519","https://openalex.org/W2963808895"],"abstract_inverted_index":{"An":[0],"ergodic":[1,58,72],"set":[2,15,42,68],"in":[3,40],"the":[4,18,41,51,57,92,97,105,110,122],"state":[5,52,137],"space":[6,53,98],"of":[7,33,47,69,79,82,87,91,99,102],"a":[8,62,67,115,131,135],"measure-preserving":[9],"dynamical":[10],"system":[11,19,93],"is":[12,20,55,94,112,119,128],"an":[13],"invariant":[14],"on":[16,26,130],"which":[17,118],"ergodic.":[21],"Moreover,":[22],"it":[23],"comprises":[24],"points":[25],"statistically":[27],"identical":[28],"trajectories,":[29],"i.e.,":[30],"time":[31,100],"averages":[32,101],"any":[34,37],"function":[35],"along":[36,104],"two":[38],"trajectories":[39],"are":[43],"equal.":[44],"The":[45,126],"collection":[46],"such":[48],"sets":[49],"partitions":[50],"and":[54],"called":[56],"partition.":[59],"We":[60],"present":[61],"computational":[63],"algorithm":[64,127],"that":[65],"retrieves":[66],"coordinates":[70,75,84],"for":[71],"sets.":[73],"Those":[74],"can":[76],"be":[77],"thought":[78],"as":[80,114],"generalization":[81],"action":[83],"from":[85],"theory":[86],"Liouville-integrable":[88],"systems.":[89],"Dynamics":[90],"embedded":[95],"into":[96],"observables":[103],"trajectories.":[106],"In":[107],"this":[108],"space,":[109],"problem":[111],"formulated":[113],"dimension-reduction":[116],"problem,":[117],"handled":[120],"by":[121],"Diffusion":[123],"Maps":[124],"algorithm.":[125],"demonstrated":[129],"2D":[132],"map":[133],"with":[134],"mixed":[136],"space.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}