{"id":"https://openalex.org/W7160320099","doi":"https://doi.org/10.48550/arxiv.2605.01864","title":"Numerical Construction of Elliptic Lower-Dimensional Quasi-Periodic Solutions with a Priori Bound","display_name":"Numerical Construction of Elliptic Lower-Dimensional Quasi-Periodic Solutions with a Priori Bound","publication_year":2026,"publication_date":"2026-05-03","ids":{"openalex":"https://openalex.org/W7160320099","doi":"https://doi.org/10.48550/arxiv.2605.01864"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.01864","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.01864","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,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.01864","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126410602","display_name":"Mingwei Fu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu, Mingwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103024187","display_name":"Bin Shi","orcid":"https://orcid.org/0000-0003-2378-5333"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Bin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11416","display_name":"Numerical methods for differential equations","score":0.5503000020980835,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.5503000020980835,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.3093999922275543,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.027699999511241913,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/perturbation","display_name":"Perturbation (astronomy)","score":0.5436000227928162},{"id":"https://openalex.org/keywords/resolvent","display_name":"Resolvent","score":0.5189999938011169},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.5033000111579895},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5020999908447266},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49219998717308044},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4603999853134155},{"id":"https://openalex.org/keywords/laurent-polynomial","display_name":"Laurent polynomial","score":0.4390000104904175},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.40299999713897705},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.391400009393692}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7311999797821045},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5436000227928162},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.5033000111579895},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5020999908447266},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49219998717308044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46959999203681946},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4603999853134155},{"id":"https://openalex.org/C106639798","wikidata":"https://www.wikidata.org/wiki/Q1701125","display_name":"Laurent polynomial","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.40299999713897705},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.391400009393692},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38909998536109924},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3133000135421753},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.30640000104904175},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3012000024318695},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.29319998621940613},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.2630000114440918}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.01864","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.01864","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,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.01864","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.01864","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,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"numerical":[1,104],"framework":[2],"for":[3,85,117],"constructing":[4],"full-dimensional":[5],"quasi-periodic":[6,51,111],"solutions":[7,52,60],"in":[8,31,41,188],"nearly":[9],"integrable":[10],"systems":[11],"was":[12],"recently":[13],"developed":[14],"by":[15,174],"Fu":[16],"and":[17,88,121],"Shi[2026].":[18],"Based":[19],"on":[20],"an":[21],"alternating":[22,103],"scheme,":[23],"this":[24,97,232],"approach":[25],"effectively":[26],"overcomes":[27],"the":[28,46,67,78,86,101,108,118,122,127,130,137,155,171,176,181,194,221,225,235,243],"secular":[29],"drift":[30],"angle":[32],"variables,":[33],"a":[34,142,149,153,164,200,239],"fundamental":[35],"limitation":[36],"of":[37,58,69,129,190,224,242],"symplectic":[38],"integrators.":[39],"However,":[40],"many":[42],"applications,":[43],"such":[44],"as":[45],"restricted":[47],"three-body":[48],"problem,":[49],"lower-dimensional":[50,110],"hold":[53],"greater":[54],"significance.":[55],"The":[56],"construction":[57],"these":[59],"is":[61,139,148],"considerably":[62],"more":[63],"challenging":[64],"due":[65],"to":[66,73,92,106],"presence":[68],"normal":[70],"frequencies,":[71],"leading":[72],"intricate":[74],"resonance":[75],"phenomena.":[76],"Beyond":[77],"subspace":[79],"resonance,":[80],"one":[81],"must":[82],"also":[83],"account":[84],"first":[87],"second":[89],"Melnikov":[90],"conditions":[91,237],"eliminate":[93],"small":[94],"divisors.":[95],"In":[96],"study,":[98],"we":[99,134,168],"extend":[100],"proposed":[102,131],"scheme":[105],"compute":[107],"elliptic":[109],"solutions.":[112],"Numerical":[113],"experiments":[114],"are":[115],"presented":[116],"H\u00e9non-Heiles":[119],"model":[120],"Fermi--Pasta--Ulam":[123],"(FPU)":[124],"model,":[125],"demonstrating":[126],"effectiveness":[128],"method.":[132],"Furthermore,":[133],"emphasize":[135],"that":[136,180,220],"perturbation":[138,157],"not":[140],"merely":[141],"polynomial":[143],"with":[144],"real":[145],"coefficients":[146],"but":[147],"real-valued":[150],"function.":[151],"As":[152],"result,":[154],"associated":[156],"operator":[158],"exhibits":[159],"Gevrey":[160,222],"decay":[161,223],"without":[162],"possessing":[163],"Hankel":[165],"structure.":[166],"Meanwhile,":[167],"further":[169],"simplify":[170],"multi-scale":[172],"analysis":[173],"exploiting":[175],"resolvent":[177],"identity,":[178],"showing":[179],"global":[182],"inverse":[183,226],"can":[184],"be":[185],"expressed":[186],"linearly":[187],"terms":[189],"local":[191],"inverses":[192],"via":[193],"gluing":[195],"procedure.":[196],"This":[197,217],"representation":[198],"reveals":[199],"regime-dependent":[201],"interaction":[202],"structure:":[203],"weak":[204],"interactions":[205,212],"dominate":[206],"at":[207,214],"short":[208],"range,":[209],"while":[210],"strong":[211],"emerge":[213],"long":[215],"range.":[216],"balance":[218],"ensures":[219],"remains":[227],"uniformly":[228],"controlled.":[229],"Moreover,":[230],"within":[231],"linear":[233],"representation,":[234],"inversion":[236],"provide":[238],"clearer":[240],"characterization":[241],"localization":[244],"properties.":[245]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-06T00:00:00"}
