{"id":"https://openalex.org/W4388723022","doi":"https://doi.org/10.1007/s00332-023-09987-x","title":"Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems","display_name":"Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems","publication_year":2023,"publication_date":"2023-11-16","ids":{"openalex":"https://openalex.org/W4388723022","doi":"https://doi.org/10.1007/s00332-023-09987-x"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-023-09987-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-023-09987-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-023-09987-x.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-023-09987-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048073268","display_name":"Samuel Jelbart","orcid":"https://orcid.org/0000-0001-8539-320X"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"S. Jelbart","raw_affiliation_strings":["Department of Mathematics, Technical University of Munich, 85748, Garching, Germany"],"raw_orcid":"https://orcid.org/0000-0001-8539-320X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Munich, 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024817853","display_name":"Christian Kuehn","orcid":"https://orcid.org/0000-0002-7063-6173"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"C. Kuehn","raw_affiliation_strings":["Department of Mathematics, Technical University of Munich, 85748, Garching, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7063-6173","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Munich, 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075355265","display_name":"Sara-Viola Kuntz","orcid":"https://orcid.org/0009-0000-4611-9742"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S.-V. Kuntz","raw_affiliation_strings":["Department of Mathematics, Technical University of Munich, 85748, Garching, Germany"],"raw_orcid":"https://orcid.org/0009-0000-4611-9742","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Munich, 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048073268"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.3049,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58867042,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"34","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9835000038146973,"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/slow-manifold","display_name":"Slow manifold","score":0.9071175456047058},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.7311826944351196},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.722285270690918},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6518114805221558},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.6168122887611389},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6151045560836792},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6059673428535461},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.584522008895874},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5376964807510376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5351454019546509},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4925273358821869},{"id":"https://openalex.org/keywords/closed-manifold","display_name":"Closed manifold","score":0.4896088242530823},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.46222153306007385},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3285002112388611},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23266631364822388},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09328633546829224}],"concepts":[{"id":"https://openalex.org/C2778671503","wikidata":"https://www.wikidata.org/wiki/Q7542110","display_name":"Slow manifold","level":3,"score":0.9071175456047058},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.7311826944351196},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.722285270690918},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6518114805221558},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.6168122887611389},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6151045560836792},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6059673428535461},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.584522008895874},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5376964807510376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5351454019546509},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4925273358821869},{"id":"https://openalex.org/C74349738","wikidata":"https://www.wikidata.org/wiki/Q1517914","display_name":"Closed manifold","level":3,"score":0.4896088242530823},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.46222153306007385},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3285002112388611},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23266631364822388},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09328633546829224},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.0},{"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/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00332-023-09987-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-023-09987-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-023-09987-x.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1763471","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1763471","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00332-023-09987-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-023-09987-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-023-09987-x.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.8399999737739563}],"awards":[{"id":"https://openalex.org/G4438527755","display_name":null,"funder_award_id":"SFB/TRR 109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6773318802","display_name":null,"funder_award_id":"TRR 109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G822936381","display_name":null,"funder_award_id":"195170736","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8876951107","display_name":null,"funder_award_id":"TRR109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320882","display_name":"Volkswagen Foundation","ror":"https://ror.org/03bsmfz84"},{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388723022.pdf"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W99189181","https://openalex.org/W176809054","https://openalex.org/W316919195","https://openalex.org/W420509224","https://openalex.org/W843153803","https://openalex.org/W1484182740","https://openalex.org/W1491439616","https://openalex.org/W1565264866","https://openalex.org/W1579475312","https://openalex.org/W1582828056","https://openalex.org/W1602468222","https://openalex.org/W1608835947","https://openalex.org/W1688235387","https://openalex.org/W1697832715","https://openalex.org/W1917539272","https://openalex.org/W1970878334","https://openalex.org/W1981961598","https://openalex.org/W1983920324","https://openalex.org/W1986739294","https://openalex.org/W1988395967","https://openalex.org/W1990972851","https://openalex.org/W2002280945","https://openalex.org/W2009734469","https://openalex.org/W2016767879","https://openalex.org/W2022997188","https://openalex.org/W2023836184","https://openalex.org/W2040791996","https://openalex.org/W2053205765","https://openalex.org/W2056702910","https://openalex.org/W2064108635","https://openalex.org/W2065087707","https://openalex.org/W2067035259","https://openalex.org/W2069773542","https://openalex.org/W2089995439","https://openalex.org/W2093823001","https://openalex.org/W2101714536","https://openalex.org/W2109607999","https://openalex.org/W2119138374","https://openalex.org/W2175339372","https://openalex.org/W2177035502","https://openalex.org/W2412480509","https://openalex.org/W2502735178","https://openalex.org/W2625456875","https://openalex.org/W2742097411","https://openalex.org/W2784017543","https://openalex.org/W2924718128","https://openalex.org/W3008606610","https://openalex.org/W3083979759","https://openalex.org/W3102637669","https://openalex.org/W3131852353","https://openalex.org/W3169355307","https://openalex.org/W3176213982","https://openalex.org/W3215922587","https://openalex.org/W3217178784","https://openalex.org/W4213302443","https://openalex.org/W4284962325","https://openalex.org/W4288075793","https://openalex.org/W4295526211","https://openalex.org/W4309210000","https://openalex.org/W4384154238"],"related_works":["https://openalex.org/W2786906736","https://openalex.org/W2070844282","https://openalex.org/W2350657230","https://openalex.org/W2950257836","https://openalex.org/W2032227660","https://openalex.org/W4388723022","https://openalex.org/W4294618979","https://openalex.org/W3152370143","https://openalex.org/W2041496883","https://openalex.org/W4229046568"],"abstract_inverted_index":{"Abstract":[0],"Geometric":[1],"singular":[2],"perturbation":[3,119,129],"theory":[4,49,269],"provides":[5],"a":[6,20,25,40,57,67,91,98,177,187,225,233],"powerful":[7],"mathematical":[8],"framework":[9],"for":[10,31,50,140,213,224,270],"the":[11,32,75,81,86,117,141,144,153,159,167,180,195,199,203,208,219,248,253,263],"analysis":[12],"of":[13,28,42,62,100,143,158,172,179,189,198,210,227,255,265,272],"\u2018stationary\u2019":[14],"multiple":[15,52],"time-scale":[16,53,102,136,155,197],"systems":[17,54,104,110,115,126,214,243],"which":[18,55,147,175,251],"possess":[19,56],"critical":[21,68],"manifold":[22,27,60,69,96],",":[23],"i.e.":[24],"smooth":[26],"steady":[29],"states":[30],"limiting":[33],"fast":[34,249],"subsystem,":[35],"particularly":[36,73],"when":[37],"combined":[38],"with":[39,105,192,215,244],"method":[41,83],"desingularisation":[43],"known":[44],"as":[45,116,127],"blow-up":[46,82,145],".":[47],"The":[48,109,134],"\u2018oscillatory\u2019":[51],"limit":[58,94],"cycle":[59,95],"instead":[61],"(or":[63],"in":[64,74,97,218,222,241,247,259],"addition":[65],"to)":[66],"is":[70,138],"less":[71],"developed,":[72],"non-normally":[76],"hyperbolic":[77],"regime.":[78],"We":[79,206],"use":[80],"to":[84,122,132,152,165,194,237,261],"analyse":[85],"global":[87,181],"oscillatory":[88,114,156],"transition":[89],"near":[90],"regular":[92],"folded":[93],"class":[99,226],"three":[101],"\u2018semi-oscillatory\u2019":[103],"two":[106,154],"small":[107],"parameters.":[108],"considered":[111],"behave":[112],"like":[113],"smallest":[118],"parameter":[120,204],"tends":[121],"zero,":[123],"and":[124,169,202],"stationary":[125],"both":[128],"parameters":[130],"tend":[131],"zero.":[133],"additional":[135],"structure":[137],"crucial":[139],"applicability":[142,209,264],"method,":[146],"cannot":[148],"be":[149],"applied":[150],"directly":[151],"counterpart":[157],"problem.":[160],"Our":[161,183],"methods":[162],"allow":[163],"us":[164],"describe":[166],"asymptotics":[168],"strong":[170],"contractivity":[171],"all":[173],"solutions":[174],"traverse":[176],"neighbourhood":[178],"singularity.":[182],"main":[184,257],"results":[185,212],"cover":[186],"range":[188],"different":[190],"cases":[191],"respect":[193],"relative":[196],"angular":[200],"dynamics":[201],"drift.":[205],"demonstrate":[207,262],"our":[211,256],"periodic":[216,245],"forcing":[217,246],"slow":[220],"equation,":[221,250],"particular":[223],"Li\u00e9nard":[228],"equations.":[229],"Finally,":[230],"we":[231],"consider":[232],"toy":[234],"model":[235],"used":[236],"study":[238],"tipping":[239],"phenomena":[240],"climate":[242],"violates":[252],"conditions":[254],"results,":[258],"order":[260],"classical":[266],"(two":[267],"time-scale)":[268],"problems":[271],"this":[273],"kind.":[274]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}