{"id":"https://openalex.org/W3105242921","doi":"https://doi.org/10.1155/2020/6864573","title":"The Existence of Invariant Tori and Quasiperiodic Solutions of the Nos\u00e9\u2013Hoover Oscillator","display_name":"The Existence of Invariant Tori and Quasiperiodic Solutions of the Nos\u00e9\u2013Hoover Oscillator","publication_year":2020,"publication_date":"2020-11-11","ids":{"openalex":"https://openalex.org/W3105242921","doi":"https://doi.org/10.1155/2020/6864573","mag":"3105242921"},"language":"en","primary_location":{"id":"doi:10.1155/2020/6864573","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/6864573","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6864573.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2020/6864573.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038831138","display_name":"Yanmin Niu","orcid":"https://orcid.org/0000-0003-3873-7393"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanmin Niu","raw_affiliation_strings":["School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China","institution_ids":["https://openalex.org/I59028903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100335146","display_name":"Xiong Li","orcid":"https://orcid.org/0000-0002-6555-9687"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiong Li","raw_affiliation_strings":["Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"],"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100335146"],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14658704,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.998199999332428,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9979000091552734,"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/T10244","display_name":"Chaos control and synchronization","score":0.9966999888420105,"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/quasiperiodic-function","display_name":"Quasiperiodic function","score":0.9305906295776367},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7343876361846924},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5240809321403503},{"id":"https://openalex.org/keywords/twist","display_name":"Twist","score":0.4986915588378906},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.43045198917388916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4029621481895447},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3203965127468109},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21719738841056824},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08407709002494812}],"concepts":[{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.9305906295776367},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7343876361846924},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5240809321403503},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.4986915588378906},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.43045198917388916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4029621481895447},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3203965127468109},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21719738841056824},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08407709002494812}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2020/6864573","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/6864573","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6864573.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:6864573","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/6864573.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:04c4e43381904a2d8ea3ad449ec1b121","is_oa":true,"landing_page_url":"https://doaj.org/article/04c4e43381904a2d8ea3ad449ec1b121","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2020/6864573","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6864573","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2020/6864573","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/6864573","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6864573.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2082826544","display_name":null,"funder_award_id":"Postdoctoral","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3493234657","display_name":null,"funder_award_id":"2020M682236","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G37568934","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4745916965","display_name":null,"funder_award_id":"11971059","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6221780053","display_name":null,"funder_award_id":"11971","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/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3105242921.pdf","grobid_xml":"https://content.openalex.org/works/W3105242921.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1975947671","https://openalex.org/W1988551773","https://openalex.org/W1994859578","https://openalex.org/W2001682419","https://openalex.org/W2017196167","https://openalex.org/W2023391208","https://openalex.org/W2031953074","https://openalex.org/W2039955557","https://openalex.org/W2067581245","https://openalex.org/W2145684950","https://openalex.org/W2191251472","https://openalex.org/W2521937322","https://openalex.org/W2567639473","https://openalex.org/W2729686873","https://openalex.org/W2791267737","https://openalex.org/W3100729812","https://openalex.org/W3101651485","https://openalex.org/W4249766803","https://openalex.org/W4292874936","https://openalex.org/W6740102095"],"related_works":["https://openalex.org/W3112195757","https://openalex.org/W2067095166","https://openalex.org/W3206287350","https://openalex.org/W2024715358","https://openalex.org/W4321392735","https://openalex.org/W1977883424","https://openalex.org/W2370487582","https://openalex.org/W2085874053","https://openalex.org/W2048399474","https://openalex.org/W2952772649"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,112],"consider":[4],"an":[5],"equivalent":[6],"form":[7],"of":[8,82,99,146],"the":[9,132,136],"Nos\u00e9\u2013Hoover":[10],"oscillator,":[11],"<math":[12,69,119],"xmlns=\"http://www.w3.org/1998/Math/MathML\"":[13,70,120],"id=\"M1\">":[14],"<msup>":[15,26,47,56],"<mrow>":[16,19,27,30,48,51,57,60],"<mi>x</mi>":[17,36],"</mrow>":[18,21,29,32,50,53,59,62],"<mo>\u2032</mo>":[20,31,52],"</msup>":[22,33,54,63],"<mo>=</mo>":[23,34,55],"<mi>y</mi>":[24,28,38,58],"<mo>,</mo>":[25,40],"<mo>\u2212</mo>":[35,37,64],"<mi>z</mi>":[39,49],"<mtext>":[41,45],"</mtext>":[42,46],"<mi":[43],"mathvariant=\"normal\">and</mi>":[44],"<mn>2</mn>":[61],"<mi>a</mi>":[65,72,122],"</math>":[66,73,123],",":[67],"where":[68],"id=\"M2\">":[71],"is":[74,85,124,150],"a":[75,80,88,97],"positive":[76],"real":[77],"parameter.":[78],"Under":[79],"series":[81],"transformations,":[83],"it":[84],"transformed":[86],"into":[87],"2-dimensional":[89],"reversible":[90,110],"system":[91,149],"about":[92,143],"action-angle":[93],"variables.":[94],"By":[95],"applying":[96],"version":[98],"twist":[100],"theorem":[101],"established":[102],"by":[103],"Liu":[104],"and":[105],"Song":[106],"in":[107],"2004":[108],"for":[109],"mappings,":[111],"find":[113],"infinitely":[114],"many":[115],"invariant":[116,137],"tori":[117,138],"whenever":[118],"id=\"M3\">":[121],"sufficiently":[125],"small,":[126],"which":[127],"eventually":[128],"turns":[129],"out":[130],"that":[131],"solutions":[133,145],"starting":[134],"on":[135],"are":[139],"quasiperiodic.":[140],"The":[141],"discussion":[142],"quasiperiodic":[144],"such":[147],"3-dimensional":[148],"relatively":[151],"new.":[152]},"counts_by_year":[],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
