{"id":"https://openalex.org/W2064398710","doi":"https://doi.org/10.1142/s0218127413500430","title":"LIMIT CYCLE BIFURCATIONS FROM CENTERS OF SYMMETRIC HAMILTONIAN SYSTEMS PERTURBED BY CUBIC POLYNOMIALS","display_name":"LIMIT CYCLE BIFURCATIONS FROM CENTERS OF SYMMETRIC HAMILTONIAN SYSTEMS PERTURBED BY CUBIC POLYNOMIALS","publication_year":2013,"publication_date":"2013-03-01","ids":{"openalex":"https://openalex.org/W2064398710","doi":"https://doi.org/10.1142/s0218127413500430","mag":"2064398710"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413500430","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500430","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1201.2709","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"ZHAOPING HU","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["CN","SI"],"is_corresponding":false,"raw_author_name":"ZHAOPING HU","raw_affiliation_strings":["Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia","Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":null,"display_name":"BIN GAO","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"BIN GAO","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":null,"display_name":"VALERY G. ROMANOVSKI","orcid":null},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"VALERY G. ROMANOVSKI","raw_affiliation_strings":["Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia","Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8278,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71752137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"03","first_page":"1350043","last_page":"1350043"},"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":0.9933000206947327,"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":0.9933000206947327,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.0010999999940395355,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.7166000008583069},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.620199978351593},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.510699987411499},{"id":"https://openalex.org/keywords/cubic-function","display_name":"Cubic function","score":0.4839000105857849},{"id":"https://openalex.org/keywords/singular-point-of-a-curve","display_name":"Singular point of a curve","score":0.4569000005722046},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.4205000102519989},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.41850000619888306},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.41600000858306885}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.7166000008583069},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.620199978351593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5845000147819519},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.510699987411499},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.486299991607666},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.4839000105857849},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.4569000005722046},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.41600000858306885},{"id":"https://openalex.org/C156903151","wikidata":"https://www.wikidata.org/wiki/Q17102788","display_name":"Ring of symmetric functions","level":4,"score":0.4129999876022339},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.3763999938964844},{"id":"https://openalex.org/C64338288","wikidata":"https://www.wikidata.org/wiki/Q2235316","display_name":"Elementary symmetric polynomial","level":4,"score":0.3635999858379364},{"id":"https://openalex.org/C91429207","wikidata":"https://www.wikidata.org/wiki/Q5192245","display_name":"Cubic form","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.33469998836517334},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.319599986076355},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C109385661","wikidata":"https://www.wikidata.org/wiki/Q11358307","display_name":"Triple system","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C24557155","wikidata":"https://www.wikidata.org/wiki/Q5583136","display_name":"Good quantum number","level":5,"score":0.28850001096725464},{"id":"https://openalex.org/C52153879","wikidata":"https://www.wikidata.org/wiki/Q930499","display_name":"Symmetric polynomial","level":4,"score":0.2867000102996826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2831999957561493},{"id":"https://openalex.org/C171436396","wikidata":"https://www.wikidata.org/wiki/Q5156499","display_name":"Complete homogeneous symmetric polynomial","level":5,"score":0.27900001406669617},{"id":"https://openalex.org/C24444364","wikidata":"https://www.wikidata.org/wiki/Q473227","display_name":"Cubic crystal system","level":2,"score":0.2635999917984009}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127413500430","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500430","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"},{"id":"pmh:oai:arXiv.org:1201.2709","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.2709","pdf_url":"https://arxiv.org/pdf/1201.2709","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1201.2709","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.2709","pdf_url":"https://arxiv.org/pdf/1201.2709","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W311778295","https://openalex.org/W1969975546","https://openalex.org/W1977739599","https://openalex.org/W1995731991","https://openalex.org/W2039576666","https://openalex.org/W2049815318","https://openalex.org/W2071479141","https://openalex.org/W2075420560","https://openalex.org/W2097813893","https://openalex.org/W2129875234"],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1,27,128],"cubic":[2,10,121,125,143],"near-Hamiltonian":[3,39,161],"systems":[4,123],"obtained":[5],"by":[6,124,141],"perturbing":[7,118,136],"a":[8,24,91,103],"symmetric":[9,15,74,120,138,142,156,160],"Hamiltonian":[11,112,122,139],"system":[12,40,113,140],"with":[13],"two":[14],"singular":[16,75,99],"points.":[17],"First,":[18],"following":[19],"[Han,":[20],"2012],":[21],"we":[22,71,105,127,145],"develop":[23],"method":[25,58],"to":[26,61,85,101],"the":[28,32,36,42,57,64,67,73,79,95,98,107,111,115,119,133,137,147,155,159,165],"analytical":[29],"property":[30],"of":[31,66,83,110,149,154,158,169],"Melnikov":[33,68],"function":[34],"near":[35,114,152],"origin":[37,43],"for":[38,81,97],"having":[41],"as":[44,167],"its":[45],"elementary":[46,88],"center":[47,89],"or":[48,90],"nilpotent":[49,92],"center.":[50,93,116,134,171],"A":[51],"computationally":[52],"efficient":[53],"algorithm":[54],"based":[55],"on":[56],"is":[59,164],"established":[60],"systematically":[62],"compute":[63],"coefficients":[65],"function.":[69],"Then,":[70],"consider":[72,146],"points":[76],"and":[77],"present":[78],"conditions":[80],"one":[82,153],"them":[84],"be":[86,102],"an":[87],"Under":[94],"condition":[96],"point":[100],"center,":[104],"obtain":[106],"standard":[108],"form":[109],"Moreover,":[117],"polynomials":[126],"limit":[129,150],"cycles":[130,151],"bifurcating":[131],"from":[132],"Finally,":[135],"polynomials,":[144],"number":[148],"centers":[157],"system,":[162],"which":[163],"same":[166],"that":[168],"another":[170]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}
