{"id":"https://openalex.org/W2168891303","doi":"https://doi.org/10.1142/s0218127413500053","title":"EIGHT LIMIT CYCLES AROUND A CENTER IN QUADRATIC HAMILTONIAN SYSTEM WITH THIRD-ORDER PERTURBATION","display_name":"EIGHT LIMIT CYCLES AROUND A CENTER IN QUADRATIC HAMILTONIAN SYSTEM WITH THIRD-ORDER PERTURBATION","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2168891303","doi":"https://doi.org/10.1142/s0218127413500053","mag":"2168891303"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413500053","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500053","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/A5100652002","display_name":"Pei Yu","orcid":"https://orcid.org/0000-0002-8848-0584"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]},{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"PEI YU","raw_affiliation_strings":["Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7, Canada","Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030649439","display_name":"Maoan Han","orcid":"https://orcid.org/0000-0001-8792-1256"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"MAOAN HAN","raw_affiliation_strings":["Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4483,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67621008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"01","first_page":"1350005","last_page":"1350005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"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/mathematics","display_name":"Mathematics","score":0.720146119594574},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.7145305871963501},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.7033248543739319},{"id":"https://openalex.org/keywords/third-order","display_name":"Third order","score":0.6585296392440796},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6419602632522583},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6365978121757507},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.617777943611145},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5819677114486694},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5682029128074646},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4987361431121826},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.49469229578971863},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.34096935391426086},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19040966033935547},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1643407642841339},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.12467390298843384},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1170191764831543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07068726420402527},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06467315554618835}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.720146119594574},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.7145305871963501},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7033248543739319},{"id":"https://openalex.org/C2777566824","wikidata":"https://www.wikidata.org/wiki/Q1259252","display_name":"Third order","level":2,"score":0.6585296392440796},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6419602632522583},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6365978121757507},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.617777943611145},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5819677114486694},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5682029128074646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4987361431121826},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.49469229578971863},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.34096935391426086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19040966033935547},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1643407642841339},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.12467390298843384},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1170191764831543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07068726420402527},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06467315554618835},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413500053","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500053","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":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W46308471","https://openalex.org/W625401248","https://openalex.org/W1593578268","https://openalex.org/W1969975546","https://openalex.org/W1982088565","https://openalex.org/W1997634909","https://openalex.org/W1998762702","https://openalex.org/W2009497399","https://openalex.org/W2011741759","https://openalex.org/W2017348434","https://openalex.org/W2039576666","https://openalex.org/W2046858619","https://openalex.org/W2049544062","https://openalex.org/W2049815318","https://openalex.org/W2053496265","https://openalex.org/W2061361830","https://openalex.org/W2072075509","https://openalex.org/W2081699720","https://openalex.org/W2096571350","https://openalex.org/W2128949314","https://openalex.org/W2129875234","https://openalex.org/W2140959905","https://openalex.org/W2148704323","https://openalex.org/W2160545686","https://openalex.org/W2163945260","https://openalex.org/W2963427501","https://openalex.org/W4237970627","https://openalex.org/W4248348571","https://openalex.org/W4293079168"],"related_works":["https://openalex.org/W2361025465","https://openalex.org/W2725010352","https://openalex.org/W2051439117","https://openalex.org/W2074183508","https://openalex.org/W2366033385","https://openalex.org/W1607517698","https://openalex.org/W4272508","https://openalex.org/W2243882821","https://openalex.org/W3103801381","https://openalex.org/W2364723928"],"abstract_inverted_index":{"In":[0],"this":[1,33,81],"paper,":[2],"we":[3],"show":[4],"that":[5,56],"generic":[6],"planar":[7,57],"quadratic":[8,58],"Hamiltonian":[9,59],"systems":[10,60],"with":[11,61],"third":[12,62],"degree":[13,63],"polynomial":[14,64],"perturbation":[15,65],"can":[16,66],"have":[17,47,67],"eight":[18],"small-amplitude":[19,71],"limit":[20,72],"cycles":[21,73],"around":[22,74],"a":[23,75,84],"center.":[24,76],"We":[25],"use":[26],"higher-order":[27,42,53],"focus":[28],"value":[29],"computation":[30,40],"to":[31,38],"prove":[32],"result,":[34],"which":[35],"is":[36,83],"equivalent":[37],"the":[39],"of":[41],"Melnikov":[43,54],"functions.":[44],"Previous":[45],"results":[46],"shown,":[48],"based":[49],"on":[50],"first-order":[51],"and":[52],"functions,":[55],"five":[68],"or":[69],"seven":[70],"The":[77],"result":[78],"given":[79],"in":[80],"paper":[82],"further":[85],"improvement.":[86]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
