{"id":"https://openalex.org/W2089198401","doi":"https://doi.org/10.1137/090760210","title":"Observing Infinite-dimensional Dynamical Systems","display_name":"Observing Infinite-dimensional Dynamical Systems","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2089198401","doi":"https://doi.org/10.1137/090760210","mag":"2089198401"},"language":"en","primary_location":{"id":"doi:10.1137/090760210","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090760210","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":["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/A5025707096","display_name":"Jessica Lin","orcid":"https://orcid.org/0000-0002-3312-7089"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jessica Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042091553","display_name":"William Ott","orcid":"https://orcid.org/0000-0002-7119-491X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William Ott","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.15987428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"9","issue":"4","first_page":"1229","last_page":"1243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9955000281333923,"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":0.9955000281333923,"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":0.9902999997138977,"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":0.9837999939918518,"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/observable","display_name":"Observable","score":0.7153608798980713},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.6959832906723022},{"id":"https://openalex.org/keywords/bar","display_name":"Bar (unit)","score":0.6379132270812988},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6127120852470398},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5916202068328857},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5803132653236389},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5449647903442383},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.5155446529388428},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4568328559398651},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.447057843208313},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.43091240525245667},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33396828174591064},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3035117983818054},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11766496300697327},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07174012064933777}],"concepts":[{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.7153608798980713},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6959832906723022},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.6379132270812988},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6127120852470398},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5916202068328857},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5803132653236389},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5449647903442383},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.5155446529388428},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4568328559398651},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.447057843208313},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.43091240525245667},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33396828174591064},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3035117983818054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11766496300697327},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07174012064933777},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090760210","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090760210","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1480681685","https://openalex.org/W1535818806","https://openalex.org/W1541939020","https://openalex.org/W1557040331","https://openalex.org/W1559403043","https://openalex.org/W1594759473","https://openalex.org/W1964897598","https://openalex.org/W1983796205","https://openalex.org/W1991014733","https://openalex.org/W1993404610","https://openalex.org/W1998609552","https://openalex.org/W2013722052","https://openalex.org/W2023590249","https://openalex.org/W2027339522","https://openalex.org/W2053486193","https://openalex.org/W2119488527","https://openalex.org/W2138320717","https://openalex.org/W2161318948","https://openalex.org/W2164634867","https://openalex.org/W2169301214","https://openalex.org/W2908064595","https://openalex.org/W4232041414"],"related_works":["https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W2379495411","https://openalex.org/W1970455529","https://openalex.org/W2034444983","https://openalex.org/W2374341159","https://openalex.org/W4206572296","https://openalex.org/W1663831515","https://openalex.org/W3158754803","https://openalex.org/W4210322350"],"abstract_inverted_index":{"We":[0,44],"study":[1],"the":[2,51,78,87],"extent":[3],"to":[4,96],"which":[5],"properties":[6],"of":[7,18,53,89,98],"infinite-dimensional":[8],"dynamical":[9],"systems":[10],"can":[11],"be":[12,23,31,38],"accurately":[13],"detected":[14],"by":[15],"examining":[16],"observations":[17],"such":[19],"systems.":[20],"Let":[21,28],"H":[22],"a":[24,32,39,61],"separable":[25],"Hilbert":[26],"space.":[27],"$f:H\\to":[29],"H$":[30,37],"map,":[33],"and":[34,69,85],"let":[35],"$A\\subset":[36],"compact":[40],"set":[41],"satisfying":[42,64],"$f(A)=A$.":[43],"prove":[45],"that,":[46],"for":[47],"almost":[48],"every":[49],"(in":[50],"sense":[52],"prevalence)":[54],"continuous":[55],"observable":[56,79],"$\\varphi:H\\to\\mathbb{R}^{M}$,":[57],"if":[58,70],"f":[59,90],"induces":[60],"map":[62,73],"$\\bar{f}$":[63,99],"$\\bar{f}\\circ\\varphi=\\varphi\\circ":[65],"f$":[66],"on":[67,83,91,100],"A":[68,92],"this":[71],"induced":[72],"has":[74],"certain":[75],"properties,":[76],"then":[77],"$\\varphi$":[80],"is":[81],"one-to-one":[82],"A,":[84],"therefore":[86],"dynamics":[88],"are":[93],"topologically":[94],"conjugate":[95],"those":[97],"$\\varphi(A)$.":[101]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
