{"id":"https://openalex.org/W3112952831","doi":"https://doi.org/10.1142/s0218127420502302","title":"The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian Systems with Polycycles S(2) or S(3) Under Perturbations of Piecewise Smooth Polynomials","display_name":"The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian Systems with Polycycles S(2) or S(3) Under Perturbations of Piecewise Smooth Polynomials","publication_year":2020,"publication_date":"2020-12-09","ids":{"openalex":"https://openalex.org/W3112952831","doi":"https://doi.org/10.1142/s0218127420502302","mag":"3112952831"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420502302","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420502302","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/A5100377435","display_name":"Jiaxin Wang","orcid":"https://orcid.org/0000-0002-6868-6809"},"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":false,"raw_author_name":"Jiaxin Wang","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Xinjiekouwai Str. 19, Beijing 100875, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Xinjiekouwai Str. 19, Beijing 100875, P. R. China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101684735","display_name":"Liqin Zhao","orcid":"https://orcid.org/0009-0007-5008-2621"},"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":"Liqin Zhao","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Xinjiekouwai Str. 19, Beijing 100875, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Xinjiekouwai Str. 19, Beijing 100875, P. R. China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101684735"],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":null,"apc_paid":null,"fwci":1.1287,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.78162232,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","issue":"15","first_page":"2050230","last_page":"2050230"},"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":0.9379000067710876,"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/mathematics","display_name":"Mathematics","score":0.7459639310836792},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5038697123527527},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4936860501766205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4769262671470642},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.47259077429771423},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.452862948179245},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43881431221961975},{"id":"https://openalex.org/keywords/annulus","display_name":"Annulus (botany)","score":0.43582555651664734},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4198223948478699},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41593965888023376},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4094995856285095},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40223732590675354},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20100712776184082},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1426672339439392},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09497445821762085}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7459639310836792},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5038697123527527},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4936860501766205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4769262671470642},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.47259077429771423},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.452862948179245},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43881431221961975},{"id":"https://openalex.org/C150936888","wikidata":"https://www.wikidata.org/wiki/Q4769748","display_name":"Annulus (botany)","level":2,"score":0.43582555651664734},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4198223948478699},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41593965888023376},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4094995856285095},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40223732590675354},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20100712776184082},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1426672339439392},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09497445821762085},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127420502302","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420502302","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":[{"id":"https://openalex.org/G4161286772","display_name":null,"funder_award_id":"11671040","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W416781817","https://openalex.org/W1968938958","https://openalex.org/W1987344369","https://openalex.org/W1992273910","https://openalex.org/W1998762702","https://openalex.org/W1999292205","https://openalex.org/W2003785155","https://openalex.org/W2007338051","https://openalex.org/W2014893614","https://openalex.org/W2033867134","https://openalex.org/W2036945994","https://openalex.org/W2046380677","https://openalex.org/W2056794517","https://openalex.org/W2117867755","https://openalex.org/W2144421062","https://openalex.org/W2169760327","https://openalex.org/W2791133188","https://openalex.org/W2891052426","https://openalex.org/W2894718329","https://openalex.org/W2922254704","https://openalex.org/W2963541050","https://openalex.org/W3034081432"],"related_works":["https://openalex.org/W2000297171","https://openalex.org/W2379021478","https://openalex.org/W4221159894","https://openalex.org/W4297058887","https://openalex.org/W2777256819","https://openalex.org/W4307280152","https://openalex.org/W4288563609","https://openalex.org/W4249930925","https://openalex.org/W4299284326","https://openalex.org/W2239880074"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"by":[3],"using":[4],"Picard\u2013Fuchs":[5],"equations":[6],"and":[7,118,127],"Chebyshev":[8],"criterion,":[9],"we":[10],"study":[11],"the":[12,32,75,81,96,100,109,113,134],"bifurcation":[13],"of":[14,34,58,99,102,108],"limit":[15,103],"cycles":[16,104],"for":[17,45],"degenerate":[18],"quadratic":[19],"Hamilton":[20],"systems":[21],"with":[22,38,64,112],"polycycles":[23],"[Formula:":[24,28,40,46,51,59,77,115,119,124,128],"see":[25,29,41,47,52,60,78,116,120,125,129],"text]":[26,30,53,61,117,121,126,130],"or":[27],"under":[31],"perturbations":[33],"piecewise":[35],"smooth":[36],"polynomials":[37],"degree":[39],"text].":[42,79],"Roughly":[43],"speaking,":[44],"text],":[48],"a":[49],"polycycle":[50],"is":[54,73,86,93],"cyclically":[55],"ordered":[56],"collection":[57],"saddles":[62],"together":[63],"orbits":[65],"connecting":[66],"them":[67],"in":[68],"specified":[69],"order.":[70],"The":[71],"discontinuity":[72],"on":[74],"line":[76],"If":[80],"first":[82],"order":[83],"Melnikov":[84],"function":[85],"not":[87],"equal":[88],"to":[89],"zero":[90],"identically,":[91],"it":[92],"proved":[94],"that":[95],"upper":[97],"bounds":[98],"number":[101],"bifurcating":[105],"from":[106],"each":[107],"period":[110],"annuli":[111],"boundary":[114],"are":[122],"respectively":[123],"(taking":[131],"into":[132],"account":[133],"multiplicity).":[135]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}