{"id":"https://openalex.org/W7214770790","doi":"https://doi.org/10.48550/arxiv.2609.33771","title":"Invariant Manifolds and Stability for Singular SPDEs","display_name":"Invariant Manifolds and Stability for Singular SPDEs","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214770790","doi":"https://doi.org/10.48550/arxiv.2609.33771"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33771","pdf_url":"https://arxiv.org/pdf/2609.33771","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.33771","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065470144","display_name":"Mazyar Ghani Varzaneh","orcid":"https://orcid.org/0000-0002-9578-2353","observed_orcids":["https://orcid.org/0000-0002-9578-2353"]},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Varzaneh, Mazyar Ghani","raw_affiliation_strings":["Fachbereich Mathematik und Statistik , Universit\u00e4t Konstanz , Konstanz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Statistik , Universit\u00e4t Konstanz , Konstanz , Germany","institution_ids":["https://openalex.org/I189712700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065470144"],"corresponding_institution_ids":["https://openalex.org/I189712700"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.39089998602867126,"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":0.39089998602867126,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.1534000039100647,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.10509999841451645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-stochastic-partial-differential-equations","display_name":"singular stochastic partial differential equations","score":0.9829999804496765},{"id":"https://openalex.org/keywords/invariant-manifolds","display_name":"invariant manifolds","score":0.8640000224113464},{"id":"https://openalex.org/keywords/stability","display_name":"stability","score":0.5270000100135803},{"id":"https://openalex.org/keywords/regularity-structures","display_name":"regularity structures","score":0.7720000147819519},{"id":"https://openalex.org/keywords/random-dynamical-systems","display_name":"random dynamical systems","score":0.984000027179718},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"ergodic theory","score":0.8259999752044678},{"id":"https://openalex.org/keywords/multiplicative-ergodic-theorem","display_name":"multiplicative ergodic theorem","score":0.8999999761581421},{"id":"https://openalex.org/keywords/lyapunov-spectrum","display_name":"Lyapunov spectrum","score":0.8820000290870667},{"id":"https://openalex.org/keywords/multiplicative-gaussian-noise","display_name":"multiplicative Gaussian noise","score":0.7599999904632568},{"id":"https://openalex.org/keywords/long-time-behavior","display_name":"long-time behavior","score":0.7829999923706055},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"exponential stability","score":0.6320000290870667},{"id":"https://openalex.org/keywords/center-manifold","display_name":"center manifold","score":0.6549999713897705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8720999956130981},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7494999766349792},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5612999796867371},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.531000018119812},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5264000296592712},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5149000287055969},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4713999927043915},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4474000036716461},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.43459999561309814},{"id":"https://openalex.org/C2779844894","wikidata":"https://www.wikidata.org/wiki/Q5421516","display_name":"Exponential dichotomy","level":3,"score":0.4300000071525574},{"id":"https://openalex.org/C193817511","wikidata":"https://www.wikidata.org/wiki/Q7291964","display_name":"Random dynamical system","level":4,"score":0.426800012588501},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.41350001096725464},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.38999998569488525},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.3815000057220459},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.3813000023365021},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.352400004863739},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3122999966144562},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.2946000099182129},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2761000096797943},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.2685999870300293},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.2671000063419342},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2653999924659729},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.26100000739097595}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33771","pdf_url":"https://arxiv.org/pdf/2609.33771","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.33771","doi":"https://doi.org/10.48550/arxiv.2609.33771","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33771","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.33771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33771","pdf_url":"https://arxiv.org/pdf/2609.33771","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5709080070","display_name":null,"funder_award_id":"516748464","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7650316851","display_name":null,"funder_award_id":"TRR 388","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214770790.pdf","grobid_xml":"https://content.openalex.org/works/W7214770790.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7204184478"],"related_works":["https://openalex.org/W4402714721","https://openalex.org/W4323651372","https://openalex.org/W2964142249","https://openalex.org/W1531441528","https://openalex.org/W4388080121","https://openalex.org/W3093842609","https://openalex.org/W3009362992","https://openalex.org/W2957857802","https://openalex.org/W115350923","https://openalex.org/W2115671991"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,19,26,37,45,58,62,67,84,98],"long-time":[3],"dynamics":[4,64],"of":[5,8,21,61,69],"a":[6,49,81,92],"class":[7],"singular":[9,46],"stochastic":[10],"partial":[11],"differential":[12],"equations":[13],"with":[14,48],"multiplicative":[15,50],"Gaussian":[16],"noise.":[17],"Using":[18],"theory":[20],"regularity":[22],"structures,":[23],"we":[24,56,90],"construct":[25],"associated":[27],"random":[28,39],"dynamical":[29],"system":[30],"and":[31,65,73],"establish":[32,66],"an":[33],"ergodic":[34,51],"framework":[35],"for":[36,44,97],"underlying":[38],"models.":[40],"Combining":[41],"pathwise":[42],"estimates":[43],"equation":[47,86],"theorem":[52],"in":[53],"Banach":[54],"spaces,":[55],"analyse":[57],"Lyapunov":[59],"spectrum":[60],"linearized":[63,85],"existence":[68],"local":[70,93],"stable,":[71,89],"unstable,":[72],"center":[74],"invariant":[75],"manifolds":[76],"around":[77],"stationary":[78],"points.":[79],"As":[80],"consequence,":[82],"when":[83],"is":[87],"exponentially":[88],"obtain":[91],"exponential":[94],"stability":[95],"result":[96],"nonlinear":[99],"equation.":[100]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
