{"id":"https://openalex.org/W7201880731","doi":"https://doi.org/10.48550/arxiv.2608.05239","title":"Persistence of invariant graphs for twist maps under analytic perturbations","display_name":"Persistence of invariant graphs for twist maps under analytic perturbations","publication_year":2026,"publication_date":"2026-08-05","ids":{"openalex":"https://openalex.org/W7201880731","doi":"https://doi.org/10.48550/arxiv.2608.05239"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.05239","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.05239","pdf_url":"https://arxiv.org/pdf/2608.05239","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.05239","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5145938092","display_name":"Qi Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Qi","raw_affiliation_strings":["School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5145934620","display_name":"Yi Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Yi","raw_affiliation_strings":["School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5145961837","display_name":"Lin Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Lin","raw_affiliation_strings":["School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125839683"],"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":0.9922000169754028,"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":0.9922000169754028,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.006000000052154064,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.00019999999494757503,"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/twist-maps","display_name":"twist maps","score":0.9570000171661377},{"id":"https://openalex.org/keywords/invariant-graphs","display_name":"invariant graphs","score":0.9800000190734863},{"id":"https://openalex.org/keywords/analytic-perturbations","display_name":"analytic perturbations","score":0.8610000014305115},{"id":"https://openalex.org/keywords/kam-theory","display_name":"KAM theory","score":0.7590000033378601},{"id":"https://openalex.org/keywords/normally-hyperbolic-invariant-manifolds","display_name":"normally hyperbolic invariant manifolds","score":0.9869999885559082},{"id":"https://openalex.org/keywords/frequency-constraints","display_name":"frequency constraints","score":0.34700000286102295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6919000148773193},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.6841999888420105},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.65829998254776},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6549999713897705},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6284000277519226},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5133000016212463},{"id":"https://openalex.org/C8522634","wikidata":"https://www.wikidata.org/wiki/Q587081","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","level":3,"score":0.5045999884605408},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43779999017715454},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.35670000314712524},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.31119999289512634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3093999922275543},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.2913999855518341},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2777999937534332}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.05239","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.05239","pdf_url":"https://arxiv.org/pdf/2608.05239","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.05239","doi":"https://doi.org/10.48550/arxiv.2608.05239","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.05239","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:2608.05239","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.05239","pdf_url":"https://arxiv.org/pdf/2608.05239","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7201880731.pdf","grobid_xml":"https://content.openalex.org/works/W7201880731.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2005265131","https://openalex.org/W6960461768","https://openalex.org/W2078697675","https://openalex.org/W4416053190","https://openalex.org/W1795227451","https://openalex.org/W2164104241","https://openalex.org/W2011419689","https://openalex.org/W3188990792","https://openalex.org/W2370645050","https://openalex.org/W3213846245"],"abstract_inverted_index":{"We":[0],"construct":[1],"high-frequency":[2],"perturbations":[3,40],"of":[4],"an":[5,13],"integrable":[6],"exact":[7],"symplectic":[8],"twist":[9],"map":[10],"which":[11],"preserve":[12],"analytic":[14],"invariant":[15],"graph":[16],"with":[17],"a":[18,45,51],"prescribed":[19],"rotation":[20],"number.":[21],"Their":[22],"oscillation":[23],"frequencies":[24],"may":[25],"be":[26],"any":[27],"positive":[28],"integers":[29],"tending":[30],"to":[31,42],"infinity.":[32],"For":[33],"every":[34],"fixed":[35],"Gevrey":[36],"parameter":[37],"$L>0$,":[38],"the":[39,59],"tend":[41],"zero":[43],"in":[44,50],"Gevrey-$\u03b1$":[46],"norm":[47],"and":[48,62],"diverge":[49],"Gevrey-$(\u03b1-\\varepsilon)$":[52],"norm.":[53],"The":[54],"frequency":[55],"class":[56],"strictly":[57],"contains":[58],"$\u03b1$-Brjuno--R\u00fcssmann":[60],"class,":[61],"their":[63],"difference":[64],"has":[65],"cardinality":[66],"\\(2^{\\aleph_0}\\).":[67]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-08T00:00:00"}
