{"id":"https://openalex.org/W7221782999","doi":"https://doi.org/10.48550/arxiv.2610.15717","title":"A Smooth Autonomous Flow with Exponential Mixing on the Three-Torus","display_name":"A Smooth Autonomous Flow with Exponential Mixing on the Three-Torus","publication_year":2026,"publication_date":"2026-10-11","ids":{"openalex":"https://openalex.org/W7221782999","doi":"https://doi.org/10.48550/arxiv.2610.15717"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.15717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15717","pdf_url":"https://arxiv.org/pdf/2610.15717","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/2610.15717","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158769877","display_name":"Nianci Jiang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiang, Nianci","raw_affiliation_strings":["Academy of Mathematics and Systems Science , Chinese Academy of Sciences , Beijing 100190 , China","School of Mathematical Sciences , University of Chinese Academy of Sciences , Beijing 100049 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science , Chinese Academy of Sciences , Beijing 100190 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"School of Mathematical Sciences , University of Chinese Academy of Sciences , Beijing 100049 , China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5158743020","display_name":"Weili Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Weili","raw_affiliation_strings":["Department of Mathematical Sciences , Tsinghua University , Beijing 100084 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Tsinghua University , Beijing 100084 , China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-mixing","display_name":"exponential mixing","score":0.9639999866485596},{"id":"https://openalex.org/keywords/3-torus","display_name":"3-torus","score":0.8399999737739563},{"id":"https://openalex.org/keywords/divergence-free-vector-fields","display_name":"divergence-free vector fields","score":0.9229999780654907},{"id":"https://openalex.org/keywords/hyperbolic-equilibria","display_name":"hyperbolic equilibria","score":0.9829999804496765},{"id":"https://openalex.org/keywords/transfer-theorem","display_name":"transfer theorem","score":0.878000020980835},{"id":"https://openalex.org/keywords/lebesgue-measure","display_name":"Lebesgue measure","score":0.7070000171661377}],"concepts":[{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.7753999829292297},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.730400025844574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7092000246047974},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.597599983215332},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.5910000205039978},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.5343999862670898},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5149000287055969},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4945000112056732},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4936999976634979},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.3695000112056732},{"id":"https://openalex.org/C105341887","wikidata":"https://www.wikidata.org/wiki/Q1307987","display_name":"Suspension (topology)","level":3,"score":0.3564000129699707},{"id":"https://openalex.org/C102224218","wikidata":"https://www.wikidata.org/wiki/Q25344559","display_name":"Exponential map (Riemannian geometry)","level":5,"score":0.3019999861717224},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.28360000252723694},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.26910001039505005},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26809999346733093}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.15717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15717","pdf_url":"https://arxiv.org/pdf/2610.15717","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.2610.15717","doi":"https://doi.org/10.48550/arxiv.2610.15717","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.15717","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.15717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15717","pdf_url":"https://arxiv.org/pdf/2610.15717","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/G3701778458","display_name":null,"funder_award_id":"12090010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6199139461","display_name":null,"funder_award_id":"12471138","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6589251086","display_name":null,"funder_award_id":"12090014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221782999.pdf","grobid_xml":"https://content.openalex.org/works/W7221782999.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W124550681","https://openalex.org/W2070417100","https://openalex.org/W2087354179","https://openalex.org/W2121864692","https://openalex.org/W2162155934","https://openalex.org/W2335484446","https://openalex.org/W2377491267","https://openalex.org/W2597608666","https://openalex.org/W2893477521","https://openalex.org/W2964314376","https://openalex.org/W3137342168","https://openalex.org/W4309826679","https://openalex.org/W4379414976","https://openalex.org/W4388490262","https://openalex.org/W4396540998","https://openalex.org/W4405909949","https://openalex.org/W4407573230","https://openalex.org/W4410872277","https://openalex.org/W4414586100","https://openalex.org/W6922252471","https://openalex.org/W6967026240","https://openalex.org/W7128168479","https://openalex.org/W7214805634"],"related_works":["https://openalex.org/W3032945202","https://openalex.org/W4309826679","https://openalex.org/W2962906663","https://openalex.org/W4416017125","https://openalex.org/W1979205550","https://openalex.org/W2075797596","https://openalex.org/W4295688158","https://openalex.org/W1734471461","https://openalex.org/W2047696387","https://openalex.org/W4295882831"],"abstract_inverted_index":{"We":[0,67],"construct":[1],"a":[2,70],"smooth":[3,26],"autonomous":[4,27],"divergence-free":[5],"vector":[6,60],"field":[7,61],"on":[8],"$\\mathbb{T}^3$":[9],"whose":[10],"flow":[11],"is":[12,54],"exponentially":[13,36],"mixing":[14,29,37,77],"with":[15],"respect":[16],"to":[17,56],"Lebesgue":[18],"measure.":[19],"This":[20],"answers":[21],"an":[22,35],"open":[23],"question":[24],"about":[25],"exponential":[28,76],"in":[30],"three":[31],"dimensions.":[32],"Starting":[33],"from":[34],"Anosov":[38],"suspension":[39],"flow,":[40],"we":[41],"perform":[42],"surgery":[43],"near":[44],"four":[45],"periodic":[46],"orbits":[47],"and":[48],"show":[49],"that":[50,74],"the":[51],"resulting":[52,59],"manifold":[53],"diffeomorphic":[55],"$\\mathbb{T}^3$.":[57],"The":[58],"has":[62],"exactly":[63],"sixteen":[64],"hyperbolic":[65],"equilibria.":[66],"also":[68],"prove":[69],"general":[71],"transfer":[72],"theorem":[73],"preserves":[75],"under":[78],"certain":[79],"singular":[80],"changes":[81],"of":[82],"coordinates.":[83]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}
