{"id":"https://openalex.org/W7220744968","doi":"https://doi.org/10.48550/arxiv.2610.05354","title":"On Algebraic-Dynamical Correspondence of Oscillatory Blow-Up Solutions for ODEs","display_name":"On Algebraic-Dynamical Correspondence of Oscillatory Blow-Up Solutions for ODEs","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220744968","doi":"https://doi.org/10.48550/arxiv.2610.05354"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05354","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05354","pdf_url":"https://arxiv.org/pdf/2610.05354","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/2610.05354","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001643425","display_name":"Kaname Matsue","orcid":"https://orcid.org/0000-0003-1143-654X","observed_orcids":["https://orcid.org/0000-0003-1143-654X"]},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]},{"id":"https://openalex.org/I4405286446","display_name":"Institute of Mathematics for Industry, Kyushu University","ror":"https://ror.org/0257yze86","country_code":"JP","type":"facility","lineage":["https://openalex.org/I135598925","https://openalex.org/I4405286446"]},{"id":"https://openalex.org/I4405287645","display_name":"International Institute for Carbon-Neutral Energy Research, Kyushu University","ror":"https://ror.org/05r6g1d09","country_code":"JP","type":"facility","lineage":["https://openalex.org/I135598925","https://openalex.org/I4405287645"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Matsue, Kaname","raw_affiliation_strings":["Institute of Mathematics for Industry , Kyushu University , Fukuoka 819-0395 , Japan","International Institute for Carbon-Neutral Energy Research (WPI-I 2 CNER) , Kyushu University , Fukuoka 819-0395 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics for Industry , Kyushu University , Fukuoka 819-0395 , Japan","institution_ids":["https://openalex.org/I135598925","https://openalex.org/I4405286446"]},{"raw_affiliation_string":"International Institute for Carbon-Neutral Energy Research (WPI-I 2 CNER) , Kyushu University , Fukuoka 819-0395 , Japan","institution_ids":["https://openalex.org/I135598925","https://openalex.org/I4405287645"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001643425"],"corresponding_institution_ids":["https://openalex.org/I135598925","https://openalex.org/I4405286446","https://openalex.org/I4405287645"],"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.002400000113993883,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0020000000949949026,"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/autonomous-equations","display_name":"autonomous ordinary differential equations","score":0.8690000176429749},{"id":"https://openalex.org/keywords/balance-laws","display_name":"balance laws","score":0.675000011920929},{"id":"https://openalex.org/keywords/periodic-solutions","display_name":"periodic solutions","score":0.578000009059906},{"id":"https://openalex.org/keywords/desingularization","display_name":"desingularization","score":0.7070000171661377},{"id":"https://openalex.org/keywords/horizon","display_name":"horizon","score":0.49000000953674316},{"id":"https://openalex.org/keywords/time-reparametrization","display_name":"time reparametrization","score":0.9829999804496765},{"id":"https://openalex.org/keywords/characteristic-multipliers","display_name":"characteristic multipliers","score":0.9620000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7980999946594238},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6262999773025513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5346999764442444},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.507099986076355},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4763999879360199},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.45249998569488525},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4269999861717224},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.42669999599456787},{"id":"https://openalex.org/C194053038","wikidata":"https://www.wikidata.org/wiki/Q7245087","display_name":"Principal part","level":2,"score":0.4219000041484833},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38420000672340393},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.37720000743865967},{"id":"https://openalex.org/C168031717","wikidata":"https://www.wikidata.org/wiki/Q1530280","display_name":"Balance (ability)","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.3327000141143799},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.29190000891685486},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C2456702","wikidata":"https://www.wikidata.org/wiki/Q1375954","display_name":"Vector-valued function","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2833999991416931},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2825999855995178},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26489999890327454},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05354","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05354","pdf_url":"https://arxiv.org/pdf/2610.05354","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.2610.05354","doi":"https://doi.org/10.48550/arxiv.2610.05354","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05354","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:2610.05354","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05354","pdf_url":"https://arxiv.org/pdf/2610.05354","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":[],"funders":[{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320335268","display_name":"Research Institute for Mathematical Sciences","ror":"https://ror.org/02kpeqv85"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220744968.pdf","grobid_xml":"https://content.openalex.org/works/W7220744968.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4408296366","https://openalex.org/W7117653693","https://openalex.org/W2891812850","https://openalex.org/W4407177478","https://openalex.org/W4309131231","https://openalex.org/W2967924488","https://openalex.org/W1963993710","https://openalex.org/W3137222138","https://openalex.org/W1988709007","https://openalex.org/W4360979714"],"abstract_inverted_index":{"We":[0,60],"develop":[1],"an":[2],"algebraic-dynamical":[3],"correspondence":[4,48,64],"for":[5,38,92],"type-I":[6,96],"oscillatory":[7],"blow-up":[8,98],"solutions":[9,19,99,103],"of":[10,20,28,65,95,104],"autonomous":[11],"ODEs":[12],"with":[13],"asymptotically":[14],"quasi-homogeneous":[15],"vector":[16,41],"fields.":[17],"Periodic":[18],"the":[21,36,39,44,47,63,77,93,105,125,131,142],"balance":[22,106,132],"law":[23,107,133],"arising":[24],"from":[25],"asymptotic":[26],"expansions":[27],"blow-ups":[29],"are":[30,81],"related":[31],"to":[32],"periodic":[33,52,97,102,117],"orbits":[34,118],"on":[35,101],"horizon":[37],"desingularized":[40],"field.":[42],"Unlike":[43],"stationary":[45],"case,":[46],"involves":[49],"a":[50,56,90],"positive":[51],"scaling":[53,71],"function":[54],"and":[55,70,108,134],"nontrivial":[57],"time":[58],"reparametrization.":[59],"further":[61],"establish":[62],"linearized":[66],"structures:":[67],"distinguished":[68],"phase":[69],"directions":[72],"generate":[73],"invariant":[74],"subbundles,":[75],"while":[76],"remaining":[78],"characteristic":[79,110],"multipliers":[80],"identified":[82],"through":[83],"associated":[84],"quotient":[85],"bundles.":[86],"These":[87],"results":[88],"yield":[89],"criterion":[91],"existence":[94],"based":[100],"their":[109],"multipliers,":[111],"without":[112],"explicitly":[113],"constructing":[114],"compactifications":[115],"or":[116],"at":[119,137],"infinity.":[120,138],"The":[121],"theory":[122],"also":[123],"clarifies":[124],"difference":[126],"between":[127],"stability":[128],"information":[129],"in":[130,135],"dynamics":[136],"Two":[139],"examples":[140],"illustrate":[141],"correspondence.":[143]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-07T00:00:00"}