{"id":"https://openalex.org/W1983863981","doi":"https://doi.org/10.1137/040618539","title":"Near Invariance for Markov Diffusion Systems","display_name":"Near Invariance for Markov Diffusion Systems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1983863981","doi":"https://doi.org/10.1137/040618539","mag":"1983863981"},"language":"en","primary_location":{"id":"doi:10.1137/040618539","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040618539","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":true,"oa_status":"green","oa_url":"https://opus.bibliothek.uni-augsburg.de/opus4/files/70803/70803.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003282971","display_name":"Fritz Colonius","orcid":"https://orcid.org/0000-0003-3853-6065"},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Fritz Colonius","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86135 Augsburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86135 Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037408236","display_name":"Tobias Gayer","orcid":null},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Gayer","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86135 Augsburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86135 Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063057216","display_name":"Wolfgang Kliemann","orcid":"https://orcid.org/0000-0002-9986-5500"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wolfgang Kliemann","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, IA 50011"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA 50011","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003282971"],"corresponding_institution_ids":["https://openalex.org/I179225836"],"apc_list":null,"apc_paid":null,"fwci":2.2276,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.87078382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"7","issue":"1","first_page":"79","last_page":"107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9958999752998352,"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":0.9958999752998352,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9909999966621399,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/controllability","display_name":"Controllability","score":0.7306884527206421},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6683967709541321},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6631559133529663},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.547429084777832},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5458053946495056},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5304237008094788},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.48418691754341125},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4838246703147888},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36633622646331787},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3654591143131256},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19841429591178894},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12456157803535461},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07432743906974792}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7306884527206421},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6683967709541321},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6631559133529663},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.547429084777832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5458053946495056},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5304237008094788},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.48418691754341125},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4838246703147888},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36633622646331787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3654591143131256},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19841429591178894},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12456157803535461},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07432743906974792},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040618539","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040618539","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:uni-augsburg.opus-bayern.de:70803","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-708031","pdf_url":"https://opus.bibliothek.uni-augsburg.de/opus4/files/70803/70803.pdf","source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.329.6632","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.6632","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-m3.ma.tum.de/foswiki/pub/M3/NCS0708/WebHome/WKconceNearInvariance-Final.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:uni-augsburg.opus-bayern.de:70803","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-708031","pdf_url":"https://opus.bibliothek.uni-augsburg.de/opus4/files/70803/70803.pdf","source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6700000166893005,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1983863981.pdf","grobid_xml":"https://content.openalex.org/works/W1983863981.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W37235499","https://openalex.org/W96968608","https://openalex.org/W161544417","https://openalex.org/W1501770280","https://openalex.org/W1539138075","https://openalex.org/W1572164227","https://openalex.org/W1575104486","https://openalex.org/W1585439360","https://openalex.org/W1594438725","https://openalex.org/W1965059791","https://openalex.org/W1975534246","https://openalex.org/W1978718596","https://openalex.org/W2001659478","https://openalex.org/W2014246467","https://openalex.org/W2021611402","https://openalex.org/W2025335914","https://openalex.org/W2031666307","https://openalex.org/W2040060987","https://openalex.org/W2042021490","https://openalex.org/W2043817082","https://openalex.org/W2045177724","https://openalex.org/W2046392353","https://openalex.org/W2051203581","https://openalex.org/W2051651145","https://openalex.org/W2063243689","https://openalex.org/W2064006352","https://openalex.org/W2079184994","https://openalex.org/W2105817384","https://openalex.org/W2128292256","https://openalex.org/W2128632834","https://openalex.org/W2133336878","https://openalex.org/W2138900442","https://openalex.org/W2144430776","https://openalex.org/W2147848673","https://openalex.org/W2150291179","https://openalex.org/W3133694715","https://openalex.org/W4255866674"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2561315646","https://openalex.org/W2332386680","https://openalex.org/W2248621902","https://openalex.org/W2003779889","https://openalex.org/W2379651310","https://openalex.org/W2113019827","https://openalex.org/W1541249122","https://openalex.org/W2413828414","https://openalex.org/W2367222340"],"abstract_inverted_index":{"A":[0],"concept":[1],"of":[2,26,33,50,65,93],"\u201cnear":[3],"invariance\u201d":[4],"is":[5,18],"developed":[6],"starting":[7],"from":[8,72],"sets":[9,39],"that":[10],"are":[11,88],"actually":[12],"invariant":[13,38,67],"under":[14,79],"smaller":[15,41],"perturbations.":[16],"This":[17,58],"based":[19],"on":[20],"a":[21,55,90],"theory":[22],"for":[23,40,62],"system":[24,95],"dynamics":[25],"Markov":[27],"diffusion":[28],"processes":[29],"illuminating":[30],"the":[31,69,76,101],"idea":[32],"\u201clarge\u201d":[34],"noise":[35,42],"perturbations":[36,87],"turning":[37],"ranges":[43],"into":[44],"transient":[45],"sets.":[46],"The":[47],"controllability":[48],"behavior":[49],"associated":[51],"deterministic":[52],"systems":[53],"plays":[54],"crucial":[56],"role.":[57],"setup":[59],"also":[60],"allows":[61],"numerical":[63],"computation":[64],"nearly":[66],"sets,":[68,74],"exit":[70,77],"times":[71],"these":[73],"and":[75,100,105],"locations":[78],"varying":[80],"perturbation":[81],"ranges.":[82],"Three":[83],"examples":[84],"with":[85,96,106],"additive":[86],"included:":[89],"one":[91],"degree":[92],"freedom":[94],"double":[97],"well":[98],"potential":[99],"escape":[102],"equation":[103],"without":[104],"periodic":[107],"excitation.":[108]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}