{"id":"https://openalex.org/W7224086060","doi":"https://doi.org/10.48550/arxiv.2610.37479","title":"Minimal acceleration and the topology of premonotonic cocycles","display_name":"Minimal acceleration and the topology of premonotonic cocycles","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224086060","doi":"https://doi.org/10.48550/arxiv.2610.37479"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.37479","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37479","pdf_url":"https://arxiv.org/pdf/2610.37479","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/2610.37479","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160017762","display_name":"Xu Xia","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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xia, Xu","raw_affiliation_strings":["State Key Laboratory of Mathematical Sciences , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , 100190 Beijing , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Mathematical Sciences , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , 100190 Beijing , P. R. China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159989429","display_name":"Jiahao Xu","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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Jiahao","raw_affiliation_strings":["State Key Laboratory of Mathematical Sciences , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , 100190 Beijing , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Mathematical Sciences , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , 100190 Beijing , P. R. China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9833999872207642,"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":0.9833999872207642,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.011900000274181366,"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":0.0006000000284984708,"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/sl-2-r-cocycles","display_name":"SL(2,R) cocycles","score":0.906000018119812},{"id":"https://openalex.org/keywords/topological-degree","display_name":"topological degree","score":0.7879999876022339},{"id":"https://openalex.org/keywords/lyapunov-exponents","display_name":"Lyapunov exponents","score":0.8550000190734863},{"id":"https://openalex.org/keywords/uniform-hyperbolicity","display_name":"uniform hyperbolicity","score":0.8989999890327454},{"id":"https://openalex.org/keywords/path-connectedness","display_name":"path-connectedness","score":0.6679999828338623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8712999820709229},{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.6693999767303467},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6103000044822693},{"id":"https://openalex.org/C135007989","wikidata":"https://www.wikidata.org/wiki/Q643156","display_name":"Rotation number","level":3,"score":0.5651000142097473},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5346999764442444},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.49559998512268066},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.47999998927116394},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45339998602867126},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.38659998774528503},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.38359999656677246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36880001425743103},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3617999851703644},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33480000495910645},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.33079999685287476},{"id":"https://openalex.org/C47600822","wikidata":"https://www.wikidata.org/wiki/Q7825032","display_name":"Topological dynamics","level":5,"score":0.32690000534057617},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.31209999322891235},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.3041999936103821},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27149999141693115},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.2671000063419342}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.37479","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37479","pdf_url":"https://arxiv.org/pdf/2610.37479","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.2610.37479","doi":"https://doi.org/10.48550/arxiv.2610.37479","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.37479","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:2610.37479","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37479","pdf_url":"https://arxiv.org/pdf/2610.37479","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/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224086060.pdf","grobid_xml":"https://content.openalex.org/works/W7224086060.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4414903162","https://openalex.org/W3037916772","https://openalex.org/W4221124064","https://openalex.org/W3144190895","https://openalex.org/W7096657896","https://openalex.org/W4411317204","https://openalex.org/W7103446366","https://openalex.org/W2886671807","https://openalex.org/W4389217709","https://openalex.org/W2589058672"],"abstract_inverted_index":{"In":[0,73,93,109],"his":[1],"global":[2],"theory":[3],"of":[4,13,30,71,87,170],"one-frequency":[5],"Schr\u00f6dinger":[6],"operators~\\cite{Av15},":[7],"Avila":[8],"asked":[9],"whether":[10,35],"the":[11,27,64,74,110,116,152,167,171],"acceleration":[12,100],"a":[14,68,81,129,137,141,175],"real-analytic":[15],"$\\SL(2,\\R)$":[16],"cocycle":[17,159],"over":[18],"an":[19,119],"irrational":[20,49,147],"circle":[21],"rotation":[22,169],"is":[23,155],"bounded":[24],"below":[25],"by":[26,90,174],"absolute":[28],"value":[29],"its":[31],"topological":[32],"degree":[33,39,173],"and":[34,104,128,149],"equality":[36],"in":[37,63,160],"nonzero":[38,94,150],"characterizes":[40],"premonotonicity.":[41,178],"We":[42],"answer":[43],"this":[44,79,161],"question":[45],"affirmatively":[46],"for":[47,144],"every":[48,158],"frequency,":[50],"without":[51],"arithmetic":[52],"restrictions.":[53],"Here":[54],"premonotonicity":[55],"means":[56],"that":[57],"some":[58],"iterate":[59],"becomes":[60],"strictly":[61],"monotonic":[62],"base":[65],"variable":[66],"after":[67],"periodic":[69,138],"change":[70],"coordinates~\\cite{AK15}.":[72],"positive":[75,106,112,121,125],"Lyapunov":[76,113],"exponent":[77,114],"regime,":[78],"provides":[80],"nonzero-degree":[82],"counterpart":[83],"to":[84,166],"Avila's":[85],"characterization":[86],"uniform":[88],"hyperbolicity":[89],"vanishing":[91],"acceleration.":[92],"degree,":[95,151],"we":[96],"also":[97],"characterize":[98],"minimal":[99],"through":[101],"signed":[102],"connections":[103],"invariant":[105,124],"matrix-valued":[107,126],"measures.":[108],"positive-degree,":[111],"case,":[115],"proof":[117],"constructs":[118],"analytic":[120],"connection":[122],"using":[123],"measures":[127],"transfer--scattering":[130],"representation.":[131],"A":[132],"complex-analytic":[133],"construction":[134],"then":[135],"produces":[136],"gauge.":[139],"As":[140],"further":[142],"consequence,":[143],"each":[145],"fixed":[146],"frequency":[148],"premonotonic":[153],"locus":[154,162],"path":[156,176],"connected:":[157],"can":[163],"be":[164],"joined":[165],"linear":[168],"same":[172],"preserving":[177]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-29T00:00:00"}
