{"id":"https://openalex.org/W2185953258","doi":null,"title":"The C 1+ hypothesis in Pesin theory revisited","display_name":"The C 1+ hypothesis in Pesin theory revisited","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2185953258","mag":"2185953258"},"language":"en","primary_location":{"id":"mag:2185953258","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1306.6391.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/1306.6391.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111803977","display_name":"Christian Bonatti","orcid":"https://orcid.org/0000-0002-2412-3414","observed_orcids":["https://orcid.org/0000-0002-2412-3414"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Bonatti","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030048112","display_name":"Sylvain Crovisier","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sylvain Crovisier","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039802453","display_name":"Katsutoshi Shinohara","orcid":"https://orcid.org/0000-0003-2448-4161","observed_orcids":["https://orcid.org/0000-0003-2448-4161"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Katsutoshi Shinohara","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2448-4161","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":4,"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/T11151","display_name":"Advanced Topology and Set Theory","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/c1-generic-diffeomorphisms","display_name":"C1-generic diffeomorphisms","score":0.703000009059906},{"id":"https://openalex.org/keywords/stable-and-unstable-manifolds","display_name":"stable and unstable manifolds","score":0.890999972820282},{"id":"https://openalex.org/keywords/compact-3-manifolds","display_name":"compact 3-manifolds","score":0.8550000190734863}],"concepts":[{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.8269472122192383},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.778099000453949},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7575520277023315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7528093457221985},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6741234064102173},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6219560503959656},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6217878460884094},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.48919227719306946},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28692126274108887},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14539620280265808},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2185953258","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1306.6391.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2185953258","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1306.6391.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1840676194","https://openalex.org/W1964759045","https://openalex.org/W2017003684","https://openalex.org/W2036955243","https://openalex.org/W2048116934","https://openalex.org/W2049415483","https://openalex.org/W2068316139","https://openalex.org/W2077969093","https://openalex.org/W2138196720","https://openalex.org/W2167364100","https://openalex.org/W2333469688","https://openalex.org/W2963961644"],"related_works":["https://openalex.org/W1990800863","https://openalex.org/W2036955243","https://openalex.org/W4392011567","https://openalex.org/W7101105376","https://openalex.org/W4414594246","https://openalex.org/W1969663512","https://openalex.org/W2057637094","https://openalex.org/W1996891734","https://openalex.org/W2890604215","https://openalex.org/W7095918987"],"abstract_inverted_index":{"We":[0,92],"show":[1],"that":[2],"for":[3],"every":[4,19,90],"compact":[5],"3-manifold":[6],"M":[7],"there":[8],"exists":[9],"an":[10,96],"open":[11],"subset":[12],"of":[13,40,46,57],"Diff":[14],"1":[15],"(M)":[16],"in":[17,54,98],"which":[18,28],"generic":[20],"diffeomorphism":[21],"admits":[22],"uncountably":[23],"many":[24],"ergodic":[25],"probability":[26],"measures":[27,59],"are":[29,34],"hyperbolic":[30],"while":[31],"their":[32],"supports":[33],"disjoint":[35],"and":[36,43,63,81],"admit":[37],"a":[38,44,50],"basis":[39,45],"attracting":[41],"neighborhoods":[42],"repelling":[47],"neighborhoods.":[48],"As":[49],"consequence,":[51],"the":[52,55,70,79,82],"points":[53],"support":[56],"these":[58],"have":[60],"no":[61,64],"stable":[62,80],"unstable":[65,83],"manifolds.":[66],"This":[67],"contrasts":[68],"with":[69,85],"higher":[71],"regularity":[72],"case,":[73],"where":[74],"Pesin":[75],"theory":[76],"gives":[77],"us":[78],"manifolds":[84],"complementary":[86],"dimensions":[87],"at":[88],"almost":[89],"point.":[91],"also":[93],"give":[94],"such":[95],"example":[97],"dimension":[99],"two,":[100],"without":[101],"local":[102],"genericity.":[103]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}
