{"id":"https://openalex.org/W2119299479","doi":"https://doi.org/10.1142/s0218127406016070","title":"BIFURCATION OF LIMIT CYCLES IN Z10-EQUIVARIANT VECTOR FIELDS OF DEGREE 9","display_name":"BIFURCATION OF LIMIT CYCLES IN Z10-EQUIVARIANT VECTOR FIELDS OF DEGREE 9","publication_year":2006,"publication_date":"2006-08-01","ids":{"openalex":"https://openalex.org/W2119299479","doi":"https://doi.org/10.1142/s0218127406016070","mag":"2119299479"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127406016070","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5078316479","display_name":"Sharon X. Wang","orcid":"https://orcid.org/0000-0002-6937-9034"},"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":"SHARON WANG","raw_affiliation_strings":["Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","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"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"PEI YU","raw_affiliation_strings":["Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100599691","display_name":"Jibin Li","orcid":"https://orcid.org/0000-0003-4839-5956"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]},{"id":"https://openalex.org/I10660446","display_name":"Kunming University of Science and Technology","ror":"https://ror.org/00xyeez13","country_code":"CN","type":"education","lineage":["https://openalex.org/I10660446"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JIBIN LI","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China","institution_ids":["https://openalex.org/I10660446"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.61,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":25,"citation_normalized_percentile":{"value":0.783394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":89},"biblio":{"volume":"16","issue":"08","first_page":"2309","last_page":"2324"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9999,"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":0.9999,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9343,"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/T10492","display_name":"Microtubule and mitosis dynamics","score":0.9094,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.8193871},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.617211},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.55925316},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.45765364}],"concepts":[{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.8193871},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7822572},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.7344059},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6787584},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.617211},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.59573853},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5763275},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.55925316},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5397661},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5082695},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.45765364},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4468207},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.41659337},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.35377544},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31806633},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17129552},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17057717},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11568409},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.06525162},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06520623},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06289318},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127406016070","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":26,"referenced_works":["https://openalex.org/W1546156674","https://openalex.org/W1553358730","https://openalex.org/W1604213221","https://openalex.org/W1964918203","https://openalex.org/W1982088565","https://openalex.org/W2016855728","https://openalex.org/W2039576666","https://openalex.org/W2044413922","https://openalex.org/W2045256358","https://openalex.org/W2049815318","https://openalex.org/W2085745427","https://openalex.org/W2089876099","https://openalex.org/W2111496031","https://openalex.org/W2128949314","https://openalex.org/W2140959905","https://openalex.org/W2160545686","https://openalex.org/W2168050314","https://openalex.org/W2787858293","https://openalex.org/W2792049198","https://openalex.org/W2974264035","https://openalex.org/W2990394733","https://openalex.org/W3040940214","https://openalex.org/W4233863580","https://openalex.org/W4237970627","https://openalex.org/W4248348571","https://openalex.org/W650460428"],"related_works":["https://openalex.org/W564736863","https://openalex.org/W3148895720","https://openalex.org/W30258475","https://openalex.org/W2364977425","https://openalex.org/W2353430195","https://openalex.org/W2349735028","https://openalex.org/W2274816674","https://openalex.org/W2071889957","https://openalex.org/W1829827914","https://openalex.org/W1813342671"],"abstract_inverted_index":{"In":[0,17],"this":[1],"paper,":[2],"we":[3,79],"consider":[4],"the":[5,60,68,74],"weakened":[6],"Hilbert's":[7],"16th":[8],"problem":[9],"for":[10],"symmetric":[11],"planar":[12,37,64],"perturbed":[13,20,38],"polynomial":[14,22,83],"Hamiltonian":[15,21,39],"systems.":[16],"particular,":[18],"a":[19,82],"vector":[23,84],"field":[24,85],"of":[25,33,46,55,63,70,76,86],"degree":[26,87],"9":[27,88,103],"is":[28,41],"studied,":[29],"and":[30,67],"an":[31],"example":[32],"Z":[34,90],"10":[35,91],"-equivariant":[36],"systems":[40,66],"constructed.":[42],"With":[43],"maximal":[44],"number":[45],"closed":[47],"orbits,":[48],"it":[49],"gives":[50],"rise":[51],"to":[52],"different":[53],"configurations":[54],"limit":[56,98],"cycles.":[57],"By":[58],"applying":[59],"bifurcation":[61],"theory":[62],"dynamic":[65],"method":[69],"detection":[71],"functions,":[72],"with":[73,89],"aid":[75],"numerical":[77],"simulations,":[78],"show":[80],"that":[81],"symmetry":[92],"can":[93],"have":[94],"at":[95],"least":[96],"80":[97],"cycles,":[99],"i.e.":[100],"H(9)":[101],"\u2265":[102],"2":[104],"-":[105],"1.":[106]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2119299479","counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2025-01-18T17:46:40.203856","created_date":"2016-06-24"}