{"id":"https://openalex.org/W4283729524","doi":"https://doi.org/10.1142/s0218127422501164","title":"Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field","display_name":"Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field","publication_year":2022,"publication_date":"2022-06-30","ids":{"openalex":"https://openalex.org/W4283729524","doi":"https://doi.org/10.1142/s0218127422501164"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127422501164","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422501164","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":true,"oa_status":"green","oa_url":"https://ddd.uab.cat/record/267147","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100443166","display_name":"Ting Chen","orcid":"https://orcid.org/0000-0001-6570-885X"},"institutions":[{"id":"https://openalex.org/I201459984","display_name":"Guangdong University Of Finances and Economics","ror":"https://ror.org/0459pv085","country_code":"CN","type":"education","lineage":["https://openalex.org/I201459984"]},{"id":"https://openalex.org/I4210149618","display_name":"Guangdong University of Finance","ror":"https://ror.org/04grzdh47","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210149618"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ting Chen","raw_affiliation_strings":["School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-6570-885X","affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China","institution_ids":["https://openalex.org/I201459984","https://openalex.org/I4210149618"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046015548","display_name":"Jaume Llibre","orcid":"https://orcid.org/0000-0002-9511-5999"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jaume Llibre","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100443166"],"corresponding_institution_ids":["https://openalex.org/I201459984","https://openalex.org/I4210149618"],"apc_list":null,"apc_paid":null,"fwci":1.6075,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.81938295,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"32","issue":"08","first_page":null,"last_page":null},"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.960099995136261,"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":0.930400013923645,"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/mathematics","display_name":"Mathematics","score":0.7099964022636414},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.7030810117721558},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.6757858991622925},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.6032443046569824},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5765799283981323},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5496637225151062},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.534742534160614},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5286655426025391},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.4683147370815277},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4672415554523468},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.41382086277008057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36439627408981323},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2042047381401062},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.14876770973205566},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12335088849067688},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.10799345374107361}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7099964022636414},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.7030810117721558},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.6757858991622925},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.6032443046569824},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5765799283981323},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5496637225151062},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.534742534160614},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5286655426025391},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.4683147370815277},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4672415554523468},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.41382086277008057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36439627408981323},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2042047381401062},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.14876770973205566},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12335088849067688},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.10799345374107361},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127422501164","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422501164","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:ddd.uab.cat:267147","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/267147","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:267147","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/267147","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"score":0.5600000023841858,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1603476693","display_name":null,"funder_award_id":"12001112","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2133003115","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G2335697406","display_name":null,"funder_award_id":"12071091","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G618704488","display_name":null,"funder_award_id":"PID2019-104658GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1968649987","https://openalex.org/W1972241390","https://openalex.org/W1974520525","https://openalex.org/W1982717554","https://openalex.org/W1986274266","https://openalex.org/W2007921277","https://openalex.org/W2022928271","https://openalex.org/W2040831324","https://openalex.org/W2041702324","https://openalex.org/W2045568967","https://openalex.org/W2046895311","https://openalex.org/W2050224274","https://openalex.org/W2063880270","https://openalex.org/W2083063620","https://openalex.org/W2089729261","https://openalex.org/W2093066289","https://openalex.org/W2115802482","https://openalex.org/W2118969162","https://openalex.org/W2340678696","https://openalex.org/W2484469314","https://openalex.org/W2500278320","https://openalex.org/W2591449019","https://openalex.org/W2767997111","https://openalex.org/W2810279415","https://openalex.org/W2888494538","https://openalex.org/W2998766904","https://openalex.org/W3204245616","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W2339458745","https://openalex.org/W2381885241","https://openalex.org/W2526407710","https://openalex.org/W2018092704","https://openalex.org/W3200065141","https://openalex.org/W1182914791","https://openalex.org/W2945028955","https://openalex.org/W3098285481","https://openalex.org/W2097333826","https://openalex.org/W2139245472"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,51,84],"study":[4],"the":[5,16,38,48,53,72],"global":[6,54],"dynamics":[7],"of":[8,25,40,43,57],"continuous":[9],"piecewise":[10,76],"quadratic":[11],"Hamiltonian":[12,45],"systems":[13,26,78],"separated":[14],"by":[15],"straight":[17],"line":[18],"[Formula:":[19,32],"see":[20,33],"text],":[21,34],"where":[22],"these":[23,58],"kinds":[24],"have":[27],"a":[28],"nilpotent":[29],"center":[30],"at":[31],"which":[35],"comes":[36],"from":[37],"combination":[39],"two":[41],"cusps":[42],"both":[44],"systems.":[46,59],"By":[47],"Poincar\u00e9":[49],"compactification":[50],"classify":[52],"phase":[55],"portraits":[56],"We":[60],"must":[61],"mention":[62],"that":[63],"it":[64],"is":[65],"extremely":[66],"rare":[67],"to":[68],"find":[69],"works":[70],"studying":[71],"center-focus":[73],"problem":[74],"in":[75],"smooth":[77],"with":[79],"nonelementary":[80],"singular":[81],"points":[82],"as":[83],"did":[85],"here.":[86]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}