{"id":"https://openalex.org/W1991001454","doi":"https://doi.org/10.1142/s021812741350123x","title":"TWO NOTES ABOUT THE ERGODICITY OF PARTIALLY HYPERBOLIC SYSTEMS","display_name":"TWO NOTES ABOUT THE ERGODICITY OF PARTIALLY HYPERBOLIC SYSTEMS","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W1991001454","doi":"https://doi.org/10.1142/s021812741350123x","mag":"1991001454"},"language":"en","primary_location":{"id":"doi:10.1142/s021812741350123x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741350123x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100953868","display_name":"Xu Lan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092223","display_name":"Suzhou Vocational University","ror":"https://ror.org/00hn8pj83","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092223"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"LAN XU","raw_affiliation_strings":["Suzhou Vocational University, Suzhou 215104, Jiangsu, P. R. China"],"affiliations":[{"raw_affiliation_string":"Suzhou Vocational University, Suzhou 215104, Jiangsu, P. R. China","institution_ids":["https://openalex.org/I4210092223"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060996139","display_name":"Beimei Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092223","display_name":"Suzhou Vocational University","ror":"https://ror.org/00hn8pj83","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092223"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"BEIMEI CHEN","raw_affiliation_strings":["Suzhou Vocational University, Suzhou 215104, Jiangsu, P. R. China"],"affiliations":[{"raw_affiliation_string":"Suzhou Vocational University, Suzhou 215104, Jiangsu, P. R. China","institution_ids":["https://openalex.org/I4210092223"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100953868"],"corresponding_institution_ids":["https://openalex.org/I4210092223"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07118673,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"07","first_page":"1350123","last_page":"1350123"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9150000214576721,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diffeomorphism","display_name":"Diffeomorphism","score":0.8802673816680908},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.8074570894241333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6874837279319763},{"id":"https://openalex.org/keywords/hyperbolic-set","display_name":"Hyperbolic set","score":0.5737907886505127},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5733294486999512},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.5320419073104858},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5047851800918579},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.5037044882774353},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.47582128643989563},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.47072187066078186},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4470745921134949},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.19549360871315002},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18460005521774292},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.059363722801208496}],"concepts":[{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.8802673816680908},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.8074570894241333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6874837279319763},{"id":"https://openalex.org/C117855890","wikidata":"https://www.wikidata.org/wiki/Q3042004","display_name":"Hyperbolic set","level":2,"score":0.5737907886505127},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5733294486999512},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5320419073104858},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5047851800918579},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.5037044882774353},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.47582128643989563},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.47072187066078186},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4470745921134949},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.19549360871315002},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18460005521774292},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.059363722801208496},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812741350123x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741350123x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W13449575","https://openalex.org/W1969663512","https://openalex.org/W1971178571","https://openalex.org/W1972136709","https://openalex.org/W2008524246","https://openalex.org/W2034061137","https://openalex.org/W2035492228","https://openalex.org/W2043927812","https://openalex.org/W2056783837","https://openalex.org/W2059199007","https://openalex.org/W2080322816","https://openalex.org/W2102683324","https://openalex.org/W2132386227","https://openalex.org/W2136787355","https://openalex.org/W2171676557","https://openalex.org/W3152478022"],"related_works":["https://openalex.org/W4387422885","https://openalex.org/W2115777931","https://openalex.org/W2089251038","https://openalex.org/W162739522","https://openalex.org/W4289549528","https://openalex.org/W2468416866","https://openalex.org/W2051823049","https://openalex.org/W1980854207","https://openalex.org/W3099023430","https://openalex.org/W2146796680"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"two":[3],"notes":[4],"about":[5],"the":[6,17,72],"ergodicity":[7,18],"of":[8,28,74],"partially":[9,25,51],"hyperbolic":[10,26,52],"systems":[11],"are":[12,61],"given.":[13],"First":[14],"one":[15,44],"is":[16,35,45,68],"for":[19,47],"a":[20,29,48,62],"C":[21,49],"2":[22,50],"volume":[23],"preserving":[24],"diffeomorphism":[27],"smooth":[30],"compact":[31],"Riemannian":[32],"manifold":[33],"which":[34],"essentially":[36],"accessible":[37],"and":[38,57],"weak":[39],"central":[40],"exponentially":[41],"bunched.":[42],"Second":[43],"that":[46],"diffeomorphism,":[53],"if":[54],"both":[55],"forward":[56],"backward":[58],"center":[59,69],"bunched":[60,70],"full":[63],"probability":[64],"set,":[65],"then":[66],"it":[67],"in":[71],"sense":[73],"[Burns":[75],"&amp;":[76],"Wilkinson,":[77],"2010].":[78]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
