{"id":"https://openalex.org/W2082605154","doi":"https://doi.org/10.1137/100795176","title":"Uniformly Hyperbolic Attractor of the Smale\u2013Williams Type for a Poincar\u00e9 Map in the Kuznetsov System","display_name":"Uniformly Hyperbolic Attractor of the Smale\u2013Williams Type for a Poincar\u00e9 Map in the Kuznetsov System","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2082605154","doi":"https://doi.org/10.1137/100795176","mag":"2082605154"},"language":"en","primary_location":{"id":"doi:10.1137/100795176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100795176","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1006.0614","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Daniel Wilczak","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Daniel Wilczak","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3337,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.92698214,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"4","first_page":"1263","last_page":"1283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.3276999890804291,"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":0.3276999890804291,"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/T10244","display_name":"Chaos control and synchronization","score":0.2142000049352646,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.17100000381469727,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.8147000074386597},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6359999775886536},{"id":"https://openalex.org/keywords/van-der-pol-oscillator","display_name":"Van der Pol oscillator","score":0.5435000061988831},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.3190999925136566},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.3100999891757965}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8147000074386597},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6359999775886536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6114000082015991},{"id":"https://openalex.org/C98010927","wikidata":"https://www.wikidata.org/wiki/Q2081515","display_name":"Van der Pol oscillator","level":3,"score":0.5435000061988831},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4334000051021576},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39739999175071716},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3783000111579895},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.3190999925136566},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C192872217","wikidata":"https://www.wikidata.org/wiki/Q720574","display_name":"R\u00f6ssler attractor","level":3,"score":0.2939000129699707},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25369998812675476}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/100795176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100795176","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1006.0614","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1006.0614","pdf_url":"https://arxiv.org/pdf/1006.0614","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,"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":"pmh:oai:ruj.uj.edu.pl:item/51684","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/51684","pdf_url":null,"source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1006.0614","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1006.0614","pdf_url":"https://arxiv.org/pdf/1006.0614","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,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1969177117","https://openalex.org/W1973273804","https://openalex.org/W1984049481","https://openalex.org/W1996476546","https://openalex.org/W2036870533","https://openalex.org/W2046964658","https://openalex.org/W2056337265","https://openalex.org/W2056755069","https://openalex.org/W2058095877","https://openalex.org/W2059226938","https://openalex.org/W2118248415","https://openalex.org/W2118382442","https://openalex.org/W2121020818","https://openalex.org/W2125566231","https://openalex.org/W2154580646","https://openalex.org/W3182252275","https://openalex.org/W4213080596"],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,16,26,30],"general":[3],"algorithm":[4],"for":[5,12,29],"computer":[6],"assisted":[7],"verification":[8],"of":[9,32,60],"uniform":[10],"hyperbolicity":[11],"maps":[13],"which":[14],"exhibit":[15],"robust":[17],"attractor.":[18],"The":[19,39],"method":[20],"has":[21,42],"been":[22,43],"successfully":[23],"applied":[24],"to":[25,58],"Poincar\u00e9":[27],"map":[28],"system":[31],"coupled":[33],"nonautonomous":[34],"van":[35],"der":[36],"Pol":[37],"oscillators.":[38],"model":[40],"equation":[41],"proposed":[44],"by":[45],"Kuznetsov":[46],"[Phys.":[47],"Rev.":[48],"Lett.,":[49],"95":[50],"(2005),":[51],"paper":[52],"144101],":[53],"and":[54],"the":[55,61],"attractor":[56],"seems":[57],"be":[59],"Smale\u2013Williams":[62],"type.":[63]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2016-06-24T00:00:00"}