{"id":"https://openalex.org/W2148714838","doi":"https://doi.org/10.1137/120889666","title":"An Iterative Method for the Approximation of Fibers in Slow-Fast Systems","display_name":"An Iterative Method for the Approximation of Fibers in Slow-Fast Systems","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2148714838","doi":"https://doi.org/10.1137/120889666","mag":"2148714838"},"language":"en","primary_location":{"id":"doi:10.1137/120889666","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120889666","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/A5012378349","display_name":"Kristian Uldall Kristiansen","orcid":"https://orcid.org/0000-0001-6090-7649"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"K. U. Kristiansen","raw_affiliation_strings":["Technical University of Denmark, Department of Applied Mathematics and Computer Science, DK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Denmark, Department of Applied Mathematics and Computer Science, DK","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090223662","display_name":"Morten Br\u00f8ns","orcid":"https://orcid.org/0000-0001-5522-3410"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"M. Br\u00f8ns","raw_affiliation_strings":["Technical University of Denmark, Department of Applied Mathematics and Computer Science, DK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Denmark, Department of Applied Mathematics and Computer Science, DK","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056304562","display_name":"Jens Starke","orcid":"https://orcid.org/0000-0001-9411-5893"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"J. Starke","raw_affiliation_strings":["Technical University of Denmark, Department of Applied Mathematics and Computer Science, DK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Denmark, Department of Applied Mathematics and Computer Science, DK","institution_ids":["https://openalex.org/I96673099"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I96673099"],"apc_list":null,"apc_paid":null,"fwci":0.6869,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.71655531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"2","first_page":"861","last_page":"900"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9994999766349792,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9994999766349792,"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":0.9980999827384949,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9962999820709229,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.6305984854698181},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5693462491035461},{"id":"https://openalex.org/keywords/fiber","display_name":"Fiber","score":0.5175301432609558},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5044475793838501},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4625477194786072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42933544516563416},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.4158555567264557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4119344651699066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3635469675064087},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3432983160018921},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1452399492263794},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.07377028465270996}],"concepts":[{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.6305984854698181},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5693462491035461},{"id":"https://openalex.org/C519885992","wikidata":"https://www.wikidata.org/wiki/Q161","display_name":"Fiber","level":2,"score":0.5175301432609558},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5044475793838501},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4625477194786072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42933544516563416},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4158555567264557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4119344651699066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3635469675064087},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3432983160018921},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1452399492263794},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07377028465270996},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120889666","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120889666","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":60,"referenced_works":["https://openalex.org/W68894988","https://openalex.org/W99189181","https://openalex.org/W104012639","https://openalex.org/W352436377","https://openalex.org/W355012799","https://openalex.org/W594166105","https://openalex.org/W619317343","https://openalex.org/W1488435683","https://openalex.org/W1518854728","https://openalex.org/W1534461957","https://openalex.org/W1562489615","https://openalex.org/W1570781945","https://openalex.org/W1638194303","https://openalex.org/W1966073621","https://openalex.org/W1966113499","https://openalex.org/W1972672965","https://openalex.org/W1980857616","https://openalex.org/W1993963075","https://openalex.org/W1997586090","https://openalex.org/W2002439637","https://openalex.org/W2005005851","https://openalex.org/W2007730534","https://openalex.org/W2009461740","https://openalex.org/W2013512541","https://openalex.org/W2019653173","https://openalex.org/W2019685954","https://openalex.org/W2024056314","https://openalex.org/W2025623727","https://openalex.org/W2029677037","https://openalex.org/W2030430503","https://openalex.org/W2032227660","https://openalex.org/W2035502912","https://openalex.org/W2045777183","https://openalex.org/W2059625173","https://openalex.org/W2061092639","https://openalex.org/W2071844352","https://openalex.org/W2089876099","https://openalex.org/W2091182946","https://openalex.org/W2101714536","https://openalex.org/W2110841752","https://openalex.org/W2132565163","https://openalex.org/W2132996009","https://openalex.org/W2134118243","https://openalex.org/W2141906015","https://openalex.org/W2160578495","https://openalex.org/W2170225574","https://openalex.org/W2171324723","https://openalex.org/W2173305634","https://openalex.org/W2591853258","https://openalex.org/W3099448176","https://openalex.org/W3101159300","https://openalex.org/W3106416878","https://openalex.org/W3123803226","https://openalex.org/W4212880698","https://openalex.org/W4237788999","https://openalex.org/W4239801441","https://openalex.org/W4241925472","https://openalex.org/W4245427449","https://openalex.org/W4255200020","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4391318723","https://openalex.org/W2101224588","https://openalex.org/W1976561797","https://openalex.org/W2322137306","https://openalex.org/W2048821739","https://openalex.org/W2013485381","https://openalex.org/W2924479417","https://openalex.org/W2364123591","https://openalex.org/W637977166","https://openalex.org/W2044398356"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,36,77],"extend":[4,78],"a":[5,69],"method":[6,26,48,67,80],"for":[7],"iteratively":[8],"improving":[9],"slow":[10],"manifolds":[11],"so":[12,82],"that":[13,83],"it":[14,84],"also":[15,62,85],"can":[16],"be":[17],"used":[18],"to":[19,29,44,64],"approximate":[20],"the":[21,41,45,52,56,66,79,87,90],"fiber":[22],"directions.":[23],"The":[24,47,59],"extended":[25],"is":[27,49],"applied":[28],"general":[30],"finite-dimensional":[31],"real":[32],"analytic":[33],"systems":[34],"where":[35],"obtain":[37],"exponential":[38],"estimates":[39],"of":[40,89],"tangent":[42],"spaces":[43],"fibers.":[46,91],"demonstrated":[50],"on":[51,68],"Michaelis--Menten--Henri":[53],"model":[54],"and":[55],"Lindemann":[57],"mechanism.":[58],"latter":[60],"example":[61],"serves":[63],"demonstrate":[65],"slow-fast":[70,74],"system":[71],"in":[72],"nonstandard":[73],"form.":[75],"Finally,":[76],"further":[81],"approximates":[86],"curvature":[88]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}